Bibliography

AB87a

G. Allasia and R. Besenghi, Numerical calculation of incomplete gamma functions by the trapezoidal rule, Numer. Math. 50 (1987), 419-428.

AB87b

G. Allasia and R. Besenghi, Numerical computation of Tricomi's psi function by the trapezoidal rule, Computing 39 (1987), 271-279.

AB89

G. Allasia and R. Besenghi, Numerical calculation of the Riemann zeta function and generalizations by means of the trapezoidal rule, Numerical and Applied Mathematics, Part 2 (Paris 1988) (C. Brezinski, ed.), IMACS Ann. Comput. Appl. Math., 1.2, Baltzer, Basel, 1989, pp. 467-472.

AB91

G. Allasia and R. Besenghi, Numerical evaluation of the Kummer function with complex argument by the trapezoidal rule, Rend. Sem. Mat. Univ. Politec. Torino 49 (1991), no. 3, 315-327 (1993).

Ach86

J.-J. Achenbach, Numerik. Implementierung von Zylinderfunktionen, Friedr. Vieweg & Sohn, Braunschweig/Wiesbaden, 1986.

ACJP85

J. Arazy, T. Claesson, S. Janson, and J. Peetre, Means and their iterations, Proceedings of the Nineteenth Nordic Congress of Mathematicians, Reykjavik 1984, Icelandic Mathematical Society, Reykjavik, 1985, pp. 191-212.

ACM

Collected algorithms from ACM, Association for Computing Machinery, 1515 Broadway, New York, New York 10036, periodically updated looseleaf collection.

ACM64

Index by subject to algorithms, 1960-63, Comm. ACM 7 (1964), 146-148.

AD79

D. E. Amos and S. L. Daniel, AMOSLIB, a special function library, version 9/77, Report 77-1390, Sandia Laboratories, August 1979.

Ada69

A. G. Adams, Algorithm 39. Areas under the normal curve, Comput. J. 12 (1969), 197-198.

ADK+84

A. A. Abramov, A. L. Dyshko, N. B. Konyukhova, T. V. Pak, and B. S. Pariiskii, Evaluation of prolate spheroidal function by solving the corresponding differential equations, U.S.S.R. Comput. Math. and Math. Phys. 24 (1984), no. 1, 1-11.

ADKL89

A. A. Abramov, A. L. Dyshko, N. B. Konyukhova, and T. V. Levitina, Evaluation of Lamé angular wave functions by solving auxiliary differential equations, U.S.S.R. Comput. Math. and Math. Phys. 29 (1989), no. 3, 119-131.

ADKL91

A. A. Abramov, A. L. Dyshko, N. B. Konyukhova, and T. V. Levitina, Computation of radial wave functions for spheroids and triaxial ellipsoids by the modified phase function method, Comput. Math. Math. Phys. 31 (1991), no. 2, 25-42.

ADW77a

D. E. Amos, S. L. Daniel, and M. K. Weston, Algorithm 511. CDC 6600 subroutines IBESS and JBESS for Bessel functions ${I}_\nu (x)$ and ${J}_\nu (x)$, $x\ge 0$, $\nu\ge 0$, ACM Trans. Math. Software 3 (1977), 93-95, for erratum see same journal v. 4 (1978), p. 411.

ADW77b

D. E. Amos, S. L. Daniel, and M. K. Weston, CDC 6600 subroutines IBESS and JBESS for Bessel functions ${I}_\nu (x)$ and ${J}_\nu (x)$, $x\ge 0$, $\nu\ge 0$, ACM Trans. Math. Software 3 (1977), 76-92.

Air84

T. J. Aird, The IMSL library, Sources and Development of Mathematical Software (W. R. Cowell, ed.), Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1984, pp. 264-301.

Alh96

Fayez A. Alhargan, A complete method for the computations of Mathieu characteristic numbers of integer orders, SIAM Rev. 38 (1996), no. 2, 239-255.

AM61

A. M. Arthurs and R. McCarroll, Expansion of spherical Bessel functions in a series of Chebyshev polynomials, Math. Comp. 15 (1961), 159-162.

AM78

R. W. B. Ardill and K. J. M. Moriarty, Spherical Bessel functions ${j}_n$ and ${y}_n$ of integer order and real argument, Comput. Phys. Comm. 14 (1978), 261-265.

Amo74

D. E. Amos, Computation of modified Bessel functions and their ratios, Math. Comp. 28 (1974), 239-251.

Amo80a

D. E. Amos, Algorithm 556. Exponential integrals, ACM Trans. Math. Software 6 (1980), 420-428, for remark see same journal v. 9 (1983), p. 525.

Amo80b

D. E. Amos, Computation of exponential integrals, ACM Trans. Math. Software 6 (1980), 365-377.

Amo83a

D. E. Amos, Algorithm 609. A portable Fortran subroutine for the Bickley functions $\operatorname{Ki}_n(x)$, ACM Trans. Math. Software 9 (1983), 480-493.

Amo83b

D. E. Amos, Algorithm 610. A portable Fortran subroutine for derivatives of the psi function, ACM Trans. Math. Software 9 (1983), 494-502.

Amo83c

D. E. Amos, Uniform asymptotic expansions for exponential integrals ${E}_n(x)$ and Bickley functions $\operatorname{Ki}_n(x)$, ACM Trans. Math. Software 9 (1983), 467-479.

Amo86

D. E. Amos, Algorithm 644. A portable package for Bessel functions of a complex argument and nonnegative order, ACM Trans. Math. Software 12 (1986), 265-273, for remarks see same journal v. 16 (1990), p. 404 and v. 21 (1995), pp. 388-393.

Amo90a

D. E. Amos, Algorithm 683. A portable Fortran subroutine for exponential integrals of a complex argument, ACM Trans. Math. Software 16 (1990), 178-182.

Amo90b

D. E. Amos, Computation of exponential integrals of a complex argument, ACM Trans. Math. Software 16 (1990), 169-177.

And82a

W. L. Anderson, Algorithm 588. Fast Hankel transforms using related and lagged convolutions, ACM Trans. Math. Software 8 (1982), 369-370.

And82b

W. L. Anderson, Fast Hankel transforms using related and lagged convolutions, ACM Trans. Math. Software 8 (1982), 344-368.

AS64

M. Abramowitz and I. A. Stegun (eds.), Handbook of mathematical functions with formulas, graphs and mathematical tables, National Bureau of Standards Applied Mathematics Series, vol. 55, U. S. Government Printing Office, Washington, D. C., 1964.

AS68

Statistical algorithms editorial note, Appl. Statist. 17 (1968), 79-82.

AS92

J. Abad and J. Sesma, Computation of Coulomb wave functions at low energies, Comput. Phys. Comm. 71 (1992), 110-124.

AS93a

R. W. Abernathy and R. P. Smith, Algorithm 724. Program to calculate $F$-percentiles, ACM Trans. Math. Software 19 (1993), 481-483.

AS93b

R. W. Abernathy and R. P. Smith, Applying series expansion to the inverse beta distribution to find percentiles of the $F$-distribution, ACM Trans. Math. Software 19 (1993), 474-480.

Ask89

R. A. Askey, Handbooks of special functions, A Century of Mathematics in America, Part III, Hist. Math., vol. 3, American Mathematical Society, Providence, Rhode Island, 1989, pp. 369-391.

ATZ83

F. M. Arscott, P. J. Taylor, and R. V. M. Zahar, On the numerical construction of ellipsoidal wave functions, Math. Comp. 40 (1983), 367-380.

Bai93

D. H. Bailey, Algorithm 719. Multiprecision translation and execution of Fortran programs, ACM Trans. Math. Software 19 (1993), 288-319.

Bak92

L. Baker, C mathematical function handbook, McGraw-Hill, Inc., New York, 1992, includes diskette.

Bar61

R. Barakat, Evaluation of the incomplete gamma function of imaginary argument by Chebyshev polynomials, Math. Comp. 15 (1961), 7-11.

Bar74

R. H. Barlow, Convergent continued fraction approximants to generalised polylogarithms, BIT 14 (1974), 112-116.

Bar76

A. R. Barnett, RCWFF--A modification of the real Coulomb wavefunction program RCWFN, Comput. Phys. Comm. 11 (1976), 141-142.

Bar81a

A. R. Barnett, An algorithm for regular and irregular Coulomb and Bessel functions of real order to machine accuracy, Comput. Phys. Comm. 21 (1981), 297-314.

Bar81b

A. R. Barnett, KLEIN: Coulomb functions for real $\lambda$ and positive energy to high accuracy, Comput. Phys. Comm. 24 (1981), 141-159.

Bar82a

A. R. Barnett, Continued-fraction evaluation of Coulomb functions ${F}_\lambda (\eta, x)$, ${G}_\lambda (\eta, x)$ and their derivatives, J. Comput. Phys. 46 (1982), 171-188.

Bar82b

A. R. Barnett, COULFG: Coulomb and Bessel functions and their derivatives, for real arguments, by Steed's method, Comput. Phys. Comm. 27 (1982), 147-166.

Bar82c

A. R. Barnett, High-precision evaluation of the regular and irregular Coulomb wavefunctions, J. Comput. Appl. Math. 8 (1982), 29-33.

BBC95

D. A. Barry, S. J. Barry, and P. J. Culligan-Hensley, Algorithm 743. WAPR: A Fortran routine for calculating real values of the ${W}$-function, ACM Trans. Math. Software 21 (1995), 172-181.

BC83a

T. A. Beu and R. I. Câmpeanu, Prolate angular spheroidal wave functions, Comput. Phys. Comm. 30 (1983), 187-192.

BC83b

T. A. Beu and R. I. Câmpeanu, Prolate radial spheroidal wave functions, Comput. Phys. Comm. 30 (1983), 177-185.

BCB95

D. A. Barry, P. J. Culligan-Hensley, and S. J. Barry, Real values of the ${W}$-function, ACM Trans. Math. Software 21 (1995), 161-171.

BD80

A. Bañuelos and R. A. Depine, A program for computing the Riemann zeta function for complex argument, Comput. Phys. Comm. 20 (1980), 441-445.

BDG+72

C. Bardin, Y. Dandeu, L. Gauthier, J. Guillerman, T. Lena, and J.-M. Pernet, Coulomb functions in the entire $(\eta, \rho)$-plane, Comput. Phys. Comm. 3 (1972), 73-87.

BDM81

A. Bañuelos, R. A. Depine, and R. C. Mancini, A program for computing the Fermi-Dirac functions, Comput. Phys. Comm. 21 (1981), 315-322.

BEGG91

D. L. Boley, S. Elhay, G. H. Golub, and M. H. Gutknecht, Nonsymmetric Lanczos and finding orthogonal polynomials associated with indefinite weights, Numer. Algorithms 1 (1991), 21-43.

BEJ76

J. M. Blair, C. A. Edwards, and J. H. Johnson, Rational Chebyshev approximations for the inverse of the error function, Math. Comp. 30 (1976), 827-830.

BEJ78

J. M. Blair, C. A. Edwards, and J. H. Johnson, Rational Chebyshev approximations for the Bickley functions $\operatorname{Ki}_n(x)$, Math. Comp. 32 (1978), 876-886.

Bel88

V. N. Belykh, Calculation on a computer of the complete elliptic integrals ${K}(x)$ and ${E}(x)$, Boundary value problems for partial differential equations, Akad. Nauk SSSR Sibirsk. Otdel., Inst. Mat., Novosibirsk, 1988, pp. 3-15, 137 (Russian).

BFST86

V. Bezvoda, R. Farzan, K. Segeth, and G. Takó, On numerical evaluation of integrals involving Bessel functions, Apl. Mat. 31 (1986), 396-410.

BG81a

G. A. Baker, Jr. and P. Graves-Morris, Padé approximants, part I, Encyclopedia of Mathematics and its Applications, vol. 13, Addison-Wesley Publishing Company, Reading, Massachusetts, 1981.

BG81b

G. A. Baker, Jr. and P. Graves-Morris, Padé approximants, part II, Encyclopedia of Mathematics and its Applications, vol. 14, Addison-Wesley Publishing Company, Reading, Massachusetts, 1981.

BGV93

K. Balla, O. S. Guk, and M. Vicsek, On the computation of Bessel functions of first kind, Computing 50 (1993), 77-85.

BH75

N. Bleistein and R. A. Handelsman, Asymptotic expansions of integrals, Holt, Rinehart and Winston, New York, 1975.

BHK91

R. F. Boisvert, S. E. Howe, and D. K. Kahaner, The guide to available mathematical software problem classification system, Comm. Statist. B--Simulation Comput. 20 (1991), 811-842.

BHKS90

R. F. Boisvert, S. E. Howe, D. K. Kahaner, and J. L. Springmann, Guide to available mathematical software, Tech. Report NISTIR 90-4237, National Institute of Standards and Technology, Center for Computing and Applied Mathematics, Gaithersburg, Maryland 20899, 1990.

Bim93

HiQ reference manual, version 2.0, Bimillennium Corporation, 16795 Lark Avenue, Suite 200, Los Gatos, California 95030, 1993.

Bis91

A. K. Bisoi, A Maple program to generate orthonormal polynomials, Comput. Math. Appl. 22 (1991), no. 9, 1-5.

BKN88a

L. V. Babushkina, M. K. Kerimov, and A. I. Nikitin, Algorithms for computing Bessel functions of half-integer order with complex arguments, U.S.S.R. Comput. Math. and Math. Phys. 28 (1988), no. 5, 109-117.

BKN88b

L. V. Babushkina, M. K. Kerimov, and A. I. Nikitin, Algorithms for evaluating spherical Bessel functions in the complex domain, U.S.S.R. Comput. Math. and Math. Phys. 28 (1988), no. 6, 122-128.

BL96

K. Balla and V. H. Linh, The simultaneous computation of Bessel functions of first and second kind, Comput. Math. Appl. 31 (1996), no. 4-5, 87-97, Selected topics in numerical methods (Miskolc, 1994).

Bla46

G. Blanch, On the computation of Mathieu functions, J. Math. and Phys. 25 (1946), 1-20.

Bla74

J. M. Blair, Rational Chebyshev approximations for the modified Bessel functions ${I}_0(x)$ and ${I}_1(x)$, Math. Comp. 28 (1974), 581-583.

BMOF92

E. Badralexe, P. Marksteiner, Y. Oh, and A. J. Freeman, Computation of the Kummer functions and Whittaker functions by using Neumann type series expansions, Comput. Phys. Comm. 71 (1992), 47-55.

BN89

J. L. Blanchard and E. H. Newman, Numerical evaluation of parabolic cylinder functions, IEEE Trans. Antennas and Propagation 37 (1989), 519-523.

Boe60

J. Boersma, Computation of Fresnel integrals, Math. Comp. 14 (1960), 380.

Bow84

K. O. Bowman, Computation of the polygamma functions, Comm. Statist. B--Simulation Comput. 13 (1984), 409-415.

BP96

R. Barakat and E. Parshall, Numerical evaluation of the zero-order Hankel transform using Filon quadrature philosophy, Appl. Math. Lett. 9 (1996), no. 5, 21-26.

BR71

R. D. Bardo and K. Ruedenberg, Numerical analysis and evaluation of normalized repeated integrals of the error function and related functions, J. Comput. Phys. 8 (1971), 167-174.

BR91

C. Brezinski and M. Redivo Zaglia, A new presentation of orthogonal polynomials with applications to their computation, Numer. Algorithms 1 (1991), 207-221.

Bra73

W. J. Braithwaite, Associated Legendre polynomials, ordinary and modified spherical harmonics, Comput. Phys. Comm. 5 (1973), 390-394.

Bre76

R. P. Brent, Fast multiple-precision evaluation of elementary functions, J. Assoc. Comput. Mach. 23 (1976), 242-251.

Bre78a

R. P. Brent, Algorithm 524. MP, a Fortran multiple-precision arithmetic package, ACM Trans. Math. Software 4 (1978), 71-81, for remark see same journal v. 5 (1979), pp. 518-519.

Bre78b

R. P. Brent, A Fortran multiple-precision arithmetic package, ACM Trans. Math. Software 4 (1978), 57-70.

Bre91

C. Brezinski, History of continued fractions and Padé approximants, Springer Series in Computational Mathematics, vol. 12, Springer-Verlag, Berlin, 1991.

Bri95

E. Brizuela, Accurate normalisation of the beta-function PDF, J. Computational Phys. 119 (1995), 385-387.

BS80

K. L. Bell and N. S. Scott, Coulomb functions (negative energies), Comput. Phys. Comm. 20 (1980), 447-458.

BS92

R. F. Boisvert and B. V. Saunders, Portable vectorized software for Bessel function evaluation, ACM Trans. Math. Software 18 (1992), 456-469, for corrigendum see same journal v. 19 (1993), p. 131.

Bui91

Bui Doan Khanh, A computation of the Fermi-Dirac integrals by asymptotics and the Hermite corrector formula, Appl. Math. Comput. 41 (1991), 61-68.

Bul65a

R. Bulirsch, Numerical calculation of elliptic integrals and elliptic functions, Numer. Math. 7 (1965), 78-90.

Bul65b

R. Bulirsch, Numerical calculation of elliptic integrals and elliptic functions. II, Numer. Math. 7 (1965), 353-354.

Bul67

R. Bulirsch, Numerical calculation of the sine, cosine and Fresnel integrals, Numer. Math. 9 (1967), 380-385.

Bul69a

R. Bulirsch, An extension of the Bartky-transformation to incomplete elliptic integrals of the third kind, Numer. Math. 13 (1969), 266-284.

Bul69b

R. Bulirsch, Numerical calculation of elliptic integrals and elliptic functions. III, Numer. Math. 13 (1969), 305-315.

Bur63

F. D. Burgoyne, Approximations to Kelvin functions, Math. Comp. 17 (1963), 295-298.

Buz84

B. L. Buzbee, The SLATEC common mathematical library, Sources and Development of Mathematical Software (W. R. Cowell, ed.), Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1984, pp. 302-320.

BvI93

C. Brezinski and J. van Iseghem, Padé approximations, Handbook of Numerical Analysis (P. G. Ciarlet and J. L. Lions, eds.), vol. 3, North-Holland, Amsterdam, 1993, in press.

BZ92

J. M. Borwein and I. J. Zucker, Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind, IMA J. Numer. Anal. 12 (1992), no. 4, 519-526.

BZ95

M. C. Bartholomew-Biggs and S. Zakovic, Using Markov's interval arithmetic to evaluate Bessel-Riccati functions, Numer. Algorithms 10 (1995), no. 3-4, 261-287.

Cal88

J. Caldwell, Computation of eigenvalues of spheroidal harmonics using relaxation, J. Phys. A 21 (1988), 3685-3693.

Cam79

J. B. Campbell, Bessel functions ${J}_{\nu}(x)$ and ${Y}_{\nu}(x)$ of real order and real argument, Comput. Phys. Comm. 18 (1979), 133-142.

Cam80

J. B. Campbell, On Temme's algorithm for the modified Bessel function of the third kind, ACM Trans. Math. Software 6 (1980), 581-586.

Cam81

J. B. Campbell, Bessel functions ${I}_\nu (z)$ and ${K}_\nu (z)$ of real order and complex argument, Comput. Phys. Comm. 24 (1981), 97-105, for erratum see same journal v. 25 (1982), p. 207.

Cam84

J. B. Campbell, Determination of $\nu$-zeros of Hankel functions, Comput. Phys. Comm. 32 (1984), 333-339.

Cam95

R. G. Campos, A quadrature formula for the Hankel transform, Numer. Algorithms 9 (1995), no. 3-4, 343-354.

Can71

J. Canosa, Numerical solution of Mathieu's equation, J. Comput. Phys. 7 (1971), 255-272.

Can81

S. M. Candel, An algorithm for the Fourier-Bessel transform, Comput. Phys. Comm. 23 (1981), 343-353.

Car65

B. C. Carlson, On computing elliptic integrals and functions, J. Math. and Phys. 44 (1965), 36-51.

Car77a

B. C. Carlson, Elliptic integrals of the first kind, SIAM J. Math. Anal. 8 (1977), 231-242.

Car77b

B. C. Carlson, Special functions of applied mathematics, Academic Press, New York, 1977.

Car79

B. C. Carlson, Computing elliptic integrals by duplication, Numer. Math. 33 (1979), 1-16.

Car87

B. C. Carlson, A table of elliptic integrals of the second kind, Math. Comp. 49 (1987), 595-606 and S13-S17.

Car88

B. C. Carlson, A table of elliptic integrals of the third kind, Math. Comp. 51 (1988), 267-280 and S1-S5.

Car89

B. C. Carlson, A table of elliptic integrals: Cubic cases, Math. Comp. 53 (1989), 327-333.

Car91

B. C. Carlson, A table of elliptic integrals: One quadratic factor, Math. Comp. 56 (1991), 267-280.

Car92

B. C. Carlson, A table of elliptic integrals: Two quadratic factors, Math. Comp. 59 (1992), 165-180.

Car95

B. C. Carlson, Numerical computation of real or complex elliptic integrals, Numer. Algorithms 10 (1995), 13-26.

CCF83

J. N. L. Connor, P. R. Curtis, and D. Farrelly, A differential equation method for the numerical evaluation of the Airy, Pearcey and swallowtail canonical integrals and their derivatives, Molecular Phys. 48 (1983), 1305-1330.

CER93

CERNLIB short writeups, CERN Program Library Office, CERN-CN Division, CH-1211 Geneva 23, Switzerland, 1993, electronic mail address is cernlib@@cernvm.cern.ch.

CF87

Ll. Closas and J. Fernández Rubio, Calculo rapido de las funciones de Bessel modificadas ${K}_{is}({X})$ e ${I}_{is}({X})$ y sus derivadas, Stochastica 11 (1987), no. 1, 53-61.

CG89

G. Chiocchia and B. Gabutti, A new transformation for computing hypergeometric series and the exact evaluation of the transonic adiabatic flow over a smooth bump, Comput. & Fluids 17 (1989), no. 1, 13-23.

CGL90

R. Coquereaux, A. Grossmann, and B. E. Lautrup, Iterative method for calculation of the Weierstrass elliptic function, IMA J. Numer. Anal. 10 (1990), 119-128.

CH67

W. J. Cody and K. E. Hillstrom, Chebyshev approximations for the natural logarithm of the gamma function, Math. Comp. 21 (1967), 198-203.

CH70a

J. A. Cochran and J. N. Hoffspiegel, Numerical techniques for finding $\nu$-zeros of Hankel functions, Math. Comp. 24 (1970), 413-422.

CH70b

W. J. Cody and K. E. Hillstrom, Chebyshev approximations for the Coulomb phase shift, Math. Comp. 24 (1970), 671-677, for corrigendum, see same journal v. 26 (1972), p. 1031.

Cha80

B. W. Char, On Stieltjes' continued fraction for the gamma function, Math. Comp. 34 (1980), 547-551.

Cha83

A. D. Chave, Numerical integration of related Hankel transforms by quadrature and continued fraction expansion, Geophysics 48 (1983), 1671-1686.

Chi92

R. C. Y. Chin, A domain decomposition method for generating orthogonal polynomials for a Gaussian weight on a finite interval, J. Comput. Phys. 99 (1992), 321-336.

Chr90

N. B. Christensen, Optimized fast Hankel transform filters, Geophys. Prospecting 38 (1990), 545-568, for comment and reply, see same journal v. 39 (1991), pp. 445-447 and 449-450.

CHT71

W. J. Cody, K. E. Hillstrom, and H. C. Thacher, Jr., Chebyshev approximations for the Riemann zeta function, Math. Comp. 25 (1971), 537-547.

CJR92

R. M. Corless, D. J. Jeffrey, and H. Rasmussen, Numerical evaluation of Airy functions with complex arguments, J. Comput. Phys. 99 (1992), 106-114.

Cle62

C. W. Clenshaw, Chebyshev series for mathematical functions, National Physical Laboratory Mathematical Tables, vol. 5, Her Majesty's Stationery Office, London, 1962.

Cle69

D. S. Clemm, Algorithm 352. Characteristic values and associated solutions of Mathieu's differential equation, Comm. ACM 12 (1969), 399-407, for remarks see same journal v. 13 (1970), p. 750 and v. 15 (1972), p. 1074.

CLM87

C. Chiccoli, S. Lorenzutta, and G. Maino, A numerical method for generalized exponential integrals, Comput. Math. Appl. 14 (1987), 261-268.

CLM88

C. Chiccoli, S. Lorenzutta, and G. Maino, On the evaluation of generalized exponential integrals ${E}_\nu (x)$, J. Comput. Phys. 78 (1988), 278-287.

CLM90a

C. Chiccoli, S. Lorenzutta, and G. Maino, An algorithm for exponential integrals of real order, Computing 45 (1990), 269-276.

CLM90b

C. Chiccoli, S. Lorenzutta, and G. Maino, Calculation of exponential integrals of real order, Internat. J. Comput. Math. 31 (1990), 125-135.

CLM90c

C. Chiccoli, S. Lorenzutta, and G. Maino, On a Tricomi series representation for the generalized exponential integral, Internat. J. Comput. Math. 31 (1990), 257-262.

CLM97

C. Chiccoli, S. Lorenzutta, and G. Maino, On the evaluation of generalized Laguerre functions, Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 131 (1997), 77-90.

CM78

J. N. L. Connor and D. C. Mackay, Accelerating the convergence of the zonal harmonic series representation in the Schumann resonance problem, J. Atmos. Terrestrial Physics 40 (1978), 977-980.

CM79

J. N. L. Connor and D. C. Mackay, Calculation of angular distributions in complex angular momentum theories of elastic scattering, Molecular Phys. 37 (1979), 1703-1712.

CM83

J. P. Coleman and A. J. Monaghan, Chebyshev expansions for the Bessel function ${J}_n(x)$ in the complex plane, Math. Comp. 40 (1983), 343-366.

CM84

A. P. Clarke and W. Marwood, A compact mathematical function package, Austral. Comput. J. 16 (1984), 107-114.

CMF77

W. J. Cody, R. M. Motley, and L. W. Fullerton, The computation of real fractional order Bessel functions of the second kind, ACM Trans. Math. Software 3 (1977), 232-239.

CMW63

C. W. Clenshaw, G. F. Miller, and M. Woodger, Algorithms for special functions I, Numer. Math. 4 (1963), 403-419.

CN81

B. C. Carlson and E. M. Notis, Algorithm 577. Algorithms for incomplete elliptic integrals, ACM Trans. Math. Software 7 (1981), 398-403.

Cod65a

W. J. Cody, Chebyshev approximations for the complete elliptic integrals ${K}$ and ${E}$, Math. Comp. 19 (1965), 105-112, for corrigenda see same journal v. 20 (1966), p. 207.

Cod65b

W. J. Cody, Chebyshev polynomial expansions of complete elliptic integrals, Math. Comp. 19 (1965), 249-259.

Cod68

W. J. Cody, Chebyshev approximations for the Fresnel integrals, Math. Comp. 22 (1968), 450-453, with Microfiche Supplement.

Cod69

W. J. Cody, Rational Chebyshev approximations for the error function, Math. Comp. 23 (1969), 631-637.

Cod70

W. J. Cody, A survey of practical rational and polynomial approximation of functions, SIAM Rev. 12 (1970), 400-423.

Cod74

W. J. Cody, The construction of numerical subroutine libraries, SIAM Rev. 16 (1974), 36-46.

Cod75

W. J. Cody, The FUNPACK package of special function routines, ACM Trans. Math. Software 1 (1975), 13-25.

Cod76

W. J. Cody, An overview of software development for special functions, Lecture Notes in Mathematics 506: Numerical Analysis Dundee, 1975 (G. A. Watson, ed.), Springer-Verlag, Berlin, 1976, pp. 38-48.

Cod80

W. J. Cody, Preliminary report on software for the modified Bessel functions of the first kind, Tech. Memorandum TM-357, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439-4801, 1980.

Cod82

W. J. Cody, Implementation and testing of function software, Lecture Notes in Computer Science No. 142. Problems and Methodologies in Mathematical Software Production (P. C. Messina and A. Murli, eds.), Springer-Verlag, Berlin, 1982, pp. 24-47.

Cod83

W. J. Cody, Algorithm 597. Sequence of modified Bessel functions of the first kind, ACM Trans. Math. Software 9 (1983), 242-245.

Cod84a

W. J. Cody, FUNPACK--A package of special function routines, Sources and Development of Mathematical Software (W. R. Cowell, ed.), Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1984, pp. 49-67.

Cod84b

W. J. Cody, Observations on the mathematical software effort, Sources and Development of Mathematical Software (W. R. Cowell, ed.), Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1984, pp. 1-19.

Cod85

W. J. Cody, Software for special functions, Rend. Sem. Mat. Univ. Politec. Torino Fascicolo Speciale. Special Functions: Theory and Computation (1985), 91-116.

Cod90a

W. J. Cody, The normal integral, Tech. Report MCS-89-1090, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439-4801, 1990.

Cod90b

W. J. Cody, Performance evaluation of programs for the error and complementary error functions, ACM Trans. Math. Software 16 (1990), 29-37.

Cod91

W. J. Cody, Performance evaluation of programs related to the real gamma function, ACM Trans. Math. Software 17 (1991), 46-54.

Cod93a

W. J. Cody, Algorithm 714. CELEFUNT: A portable test package for complex elementary functions, ACM Trans. Math. Software 19 (1993), 1-21.

Cod93b

W. J. Cody, Algorithm 715. SPECFUN: A portable Fortran package of special function routines and test drivers, ACM Trans. Math. Software 19 (1993), 22-32, for remark see same journal v. 22 (1996), p. 258.

Cof91

M. W. Coffey, Calculation of generalized Lommel integrals for modified Bessel functions, J. Phys. A 24 (1991), 23-33.

Col80

J. P. Coleman, A Fortran subroutine for the Bessel function ${J}_n(x)$ of order 0 to 10, Comput. Phys. Comm. 21 (1980), 109-118.

Col87a

J. P. Coleman, Complex polynomial approximation by the Lanczos $\tau$-method: Dawson's integral, J. Comput. Appl. Math. 20 (1987), 137-151.

Col87b

J. P. Coleman, Polynomial approximations in the complex plane, J. Comput. Appl. Math. 18 (1987), 193-211.

Coo68

B. E. Cooper, Algorithm AS 10. The use of orthogonal polynomials, Appl. Statist. 17 (1968), 283-287.

Cor72

P. Cornille, Computation of Hankel transforms, SIAM Rev. 14 (1972), 278-285.

COT89

C. W. Clenshaw, F. W. J. Olver, and P. R. Turner, Level-index arithmetic: An introductory survey, Lecture Notes in Mathematics 1397: Numerical Analysis and Parallel Processing (Lancaster 1987) (P. R. Turner, ed.), Springer-Verlag, Berlin, 1989, pp. 95-168.

CP66

C. W. Clenshaw and S. M. Picken, Chebyshev series for Bessel functions of fractional order, National Physical Laboratory Mathematical Tables, vol. 8, Her Majesty's Stationery Office, London, 1966.

P98

P. ársky and M. Polášek, Incomplete gamma ${F}\sb m(x)$ functions for real negative and complex arguments, J. Computational Phys. 143 (1998), 259-265.

CPC84

Master index volumes 1-30, July 1969--December 1983, Comput. Phys. Comm. 35 (1984), B1-B75, C1-C928.

CPC87

Program master index volumes 1-40, July 1969--June 1986, Comput. Phys. Comm. (1987), 1-75.

CPC90

Master index volumes 41-50, July 1986--July 1988, Comput. Phys. Comm. (1990), 17-30.

CPT70

W. J. Cody, K. A. Paciorek, and H. C. Thacher, Jr., Chebyshev approximations for Dawson's integral, Math. Comp. 24 (1970), 171-178.

Cra94

Isabella Cravero, The computation of the zeros of Laguerre polynomials, Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 128 (1994), no. 3-4, 105-115 (1995).

Cra98

R. E. Crandall, Fast evaluation of multiple zeta sums, Math. Comp. 67 (1998), 1163-1172.

Cri89

C. L. Critchfield, Computation of elliptic functions, J. Math. Phys. 30 (1989), 295-297.

CS89

W. J. Cody and L. Stoltz, Performance evaluation of programs for certain Bessel functions, ACM Trans. Math. Software 15 (1989), 41-48.

CS91

W. J. Cody and L. Stoltz, The use of Taylor series to test accuracy of function programs, ACM Trans. Math. Software 17 (1991), 55-63.

CS93

A. S. Clarke and B. Shizgal, On the generation of orthogonal polynomials using asymptotic methods for recurrence coefficients, J. Computational Phys. 104 (1993), 140-149.

CS97

R. Chattamvelli and R. Shanmugam, Algorithm AS 310. Computing the non-central beta distribution function, Appl. Statist. 46 (1997), 146-156.

CST73

W. J. Cody, A. J. Strecok, and H. C. Thacher, Jr., Chebyshev approximations for the psi function, Math. Comp. 27 (1973), 123-127.

CT67

W. J. Cody and H. C. Thacher, Jr., Rational Chebyshev approximations for Fermi-Dirac integrals of orders $-1/2$, $1/2$ and $3/2$, Math. Comp. 21 (1967), 30-40.

CT68

W. J. Cody and H. C. Thacher, Jr., Rational Chebyshev approximations for the exponential integral ${E}_1(x)$, Math. Comp. 22 (1968), 641-649.

CT69

W. J. Cody and H. C. Thacher, Jr., Chebyshev approximations for the exponential integral $\operatorname{Ei}(x)$, Math. Comp. 23 (1969), 289-303.

CT85

M. Carmignani and A. Tortorici Macaluso, Calcolo delle funzioni speciali ${\Gamma}(x)$, $\log {\Gamma}(x)$, ${\beta}(x,y)$, $\operatorname{erf}(x)$, $\operatorname{erfc}(x)$ alle alte precisioni, Atti Accad. Sci. Lett. Arti Palermo Ser. (5) 2 (1981-82) (1985), no. 1, 7-25.

CT94

J. A. Christley and I. J. Thompson, CRCWFN: coupled real Coulomb wavefunctions, Comput. Phys. Comm. 79 (1994), 143-155.

Cun69

S. W. Cunningham, Algorithm AS 24. From normal integral to deviate, Appl. Statist. 18 (1969), 290-293.

CW80

W. J. Cody and W. Waite, Software manual for the elementary functions, Prentice Hall, Englewood Cliffs, New Jersey, 1980.

Del73

Delft Numerical Analysis Group, On the computation of Mathieu functions, J. Engrg. Math. 7 (1973), 39-61.

Del79

G. Delic, Chebyshev expansion of the associated Legendre polynomial ${P}_{L}^{M} (x)$, Comput. Phys. Comm. 18 (1979), 63-71.

dIVPM95

C. de Izarra, O. Vallée, J. Picart, and N. T. Minh, Computation of the Whittaker functions ${W}_{\kappa,\mu}(z)$ with series expansions and Padé approximants, Comput. in Phys. 9 (1995), no. 3, 318-323.

DJ67

A. R. DiDonato and M. P. Jarnagin, The efficient calculation of the incomplete beta-function ratio for half-integer values of the parameters $a,b$, Math. Comp. 21 (1967), 652-662.

DK90

S. L. Dvorak and E. F. Kuester, Numerical computation of the incomplete Lipschitz-Hankel integral $\operatorname{Je}@,_0(a,z)$, J. Comput. Phys. 87 (1990), 301-327.

DKK81

V. A. Ditkin, K. A. Karpov, and M. K. Kerimov, The computation of special functions, U.S.S.R. Comput. Math. and Math. Phys. 20 (1981), no. 5, 3-12.

DM86

A. R. DiDonato and A. H. Morris, Jr., Computation of the incomplete gamma function ratios and their inverse, ACM Trans. Math. Software 12 (1986), 377-393.

DM87

A. R. DiDonato and A. H. Morris, Jr., Algorithm 654. Fortran subroutines for computing the incomplete gamma function ratios and their inverse, ACM Trans. Math. Software 13 (1987), 318-319.

DM92

A. R. DiDonato and A. H. Morris, Jr., Algorithm 708. Significant digit computation of the incomplete beta function ratios, ACM Trans. Math. Software 18 (1992), 360-373, for certification see same journal v. 20 (1994), pp. 393-397.

DNM96

T. Do-Nhat and R. H. MacPhie, On the accurate computation of the prolate spheroidal radial functions of the second kind, Quart. Appl. Math. 54 (1996), no. 4, 677-685.

Dor68

E. Dorrer, Algorithm 322. $F$-distribution, Comm. ACM 11 (1968), 116-117, for certification see same journal v. 12 (1969), p. 39.

DR94a

C. F. Dunkl and D. E. Ramirez, Algorithm 736. Hyperelliptic integrals and the surface measure of ellipsoids, ACM Trans. Math. Software 20 (1994), 427-435.

DR94b

C. F. Dunkl and D. E. Ramirez, Computing hyperelliptic integrals for surface measure of ellipsoids, ACM Trans. Math. Software 20 (1994), 413-426.

DR98

H.-J. Dobner and S. Ritter, Verified computation of Lamé functions with high accuracy, Computing 60 (1998), 81-89.

dT93

C. F. du Toit, Bessel functions ${J}\sb n(z)$ and ${Y}\sb n(z)$ of integer order and complex argument, Comput. Phys. Comm. 78 (1993), no. 1-2, 181-189.

DW95

K. Devlin and N. Wilson, Six-year index of ``Computers and Mathematics'', Notices Amer. Math. Soc. 42 (1995), 248-254.

Eck76

U. Eckhardt, A rational approximation to Weierstrass' $\mathcal{P}$-function, Math. Comp. 30 (1976), 818-826.

Eck77

U. Eckhardt, A rational approximation to Weierstrass' $\mathcal{P}$-function. II. The lemniscatic case, Computing 18 (1977), 341-349.

Eck80

U. Eckhardt, Algorithm 549. Weierstrass' elliptic functions, ACM Trans. Math. Software 4 (1980), 112-120.

Egl84

A. P. Eglaya, Eigenvalues of wave spheroidal functions with a complex parameter, Latv. Mat. Ezhegodnik (1984), no. 28, 143-150 (Russian).

Ehr95

U. T. Ehrenmark, The numerical inversion of two classes of Kontorovich-Lebedev transform by direct quadrature, J. Comput. Appl. Math. 61 (1995), 43-72.

EK92

Ö. Eeciolu and Ç. K. Koç, A parallel algorithm for generating discrete orthogonal polynomials, Parallel Comput. 18 (1992), 649-659.

EKK85

A. Yu. Eremin, I. E. Kaporin, and M. K. Kerimov, The calculation of the Riemann zeta-function in the complex domain, U.S.S.R. Comput. Math. and Math. Phys. 25 (1985), no. 2, 111-119, see also [YKK88].

EMOT53a

A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher transcendental functions, vol. 1, McGraw-Hill, New York, 1953, reprinted and published in 1981 by Krieger Publishing Company, Melbourne, Florida.

EMOT53b

A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher transcendental functions, vol. 2, McGraw-Hill, New York, 1953, reprinted and published in 1981 by Krieger Publishing Company, Melbourne, Florida.

EMOT55

A. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher transcendental functions, vol. 3, McGraw-Hill, New York, 1955, reprinted and published in 1981 by Krieger Publishing Company, Melbourne, Florida.

EP69

S. P. Eraševskaja and A. A. Pal'cev, The computation of spheroidal functions and their first derivatives on a computer. II, Vesc Akad. Navuk BSSR Ser. Fz.-Mat. Navuk (1969), no. 4, 37-46 (Russian).

Eva74

D. J. Evans (ed.), Software for numerical mathematics, Proceedings of the Loughboro University of Technology Conference of the IMA held in April 1973, Academic Press, London, 1974.

EWB84

A. S. Elder, J. N. Walbert, and E. C. Benck, Calculation of Legendre functions on the cut for integral order and complex degree by means of Gauss continued fractions, Tech. Report ARBRL-MR-03335, U. S. Army Armament Research and Development Center, Ballistic Research Laboratory, Aberdeen Proving Ground, Maryland, 1984, copies obtainable from National Technical Information Service, U. S. Dept. of Commerce, Springfield, VA 22161.

Fet70

H. E. Fettis, A new method for computing toroidal harmonics, Math. Comp. 24 (1970), 667-670.

Feu91

F. Feuillebois, Numerical calculation of singular integrals related to Hankel transform, Comput. Math. Appl. 21 (1991), no. 2-3, 87-94.

FG91

B. Fischer and G. H. Golub, On generating polynomials which are orthogonal over several intervals, Math. Comp. 56 (1991), 711-730.

FG92

B. Fischer and G. H. Golub, How to generate unknown orthogonal polynomials out of known orthogonal polynomials, J. Comput. Appl. Math. 43 (1992), 99-115.

FGG82

J. D. Fenton and R. S. Gardiner-Garden, Rapidly-convergent methods for evaluating elliptic integrals and theta and elliptic functions, J. Austral. Math. Soc. Ser. B 24 (1982), 47-58.

FHS78a

P. A. Fox, A. D. Hall, and N. L. Schryer, Algorithm 528. Framework for a portable library, ACM Trans. Math. Software 4 (1978), 177-188.

FHS78b

P. A. Fox, A. D. Hall, and N. L. Schryer, The PORT mathematical subroutine library, ACM Trans. Math. Software 4 (1978), 104-126.

FI94

Toshio Fukushima and Hideharu Ishizaki, Numerical computation of incomplete elliptic integrals of a general form, Celestial Mech. Dynam. Astronom. 59 (1994), no. 3, 237-251.

Fik68

C. T. Fike, Computer evaluation of mathematical functions, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1968.

FL67

W. G. Fair and Y. L. Luke, Rational approximations to the incomplete elliptic integrals of the first and second kinds, Math. Comp. 21 (1967), 418-422.

Fle68

O. L. Fleckner, A method for the computation of the Fresnel integrals and related functions, Math. Comp. 22 (1968), 635-640.

FO94

H. Früchtl and P. Otto, A new algorithm for the evaluation of the incomplete gamma function on vector computers, ACM Trans. Math. Software 20 (1994), 436-446.

For97

R. C. Forrey, Computing the hypergeometric function, J. Computational Phys. 137 (1997), 79-100.

Fox56

L. Fox, The use and construction of mathematical tables, National Physical Laboratory Mathematical Tables, vol. 1, Her Majesty's Stationery Office, London, 1956.

Fox84

P. A. Fox, The PORT mathematical subroutine library, Sources and Development of Mathematical Software (W. R. Cowell, ed.), Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1984, pp. 346-374.

FP68

L. Fox and I. B. Parker, Chebyshev polynomials in numerical analysis, Oxford University Press, London, 1968.

FP84

B. Ford and J. C. T. Pool, The evolving NAG library service, Sources and Development of Mathematical Software (W. R. Cowell, ed.), Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1984, pp. 375-397.

FR86

L. W. Fullerton and G. A. Rinker, Generalized Fermi-Dirac integrals--FD, FDG, FDH, Comput. Phys. Comm. 39 (1986), 181-185.

FS67

A. M. S. Filho and G. Schwachheim, Algorithm 309. Gamma function with arbitrary precision, Comm. ACM 10 (1967), 511-512.

Ful72

L. W. Fullerton, Algorithm 435. Modified incomplete gamma function, Comm. ACM 15 (1972), 993-995, for remark see ACM Trans. Math. Software v. 4 (1978), pp. 296-304.

Ful77

L. W. Fullerton, Portable special function routines, Lecture Notes in Computer Science 57: Portability of Numerical Software (Oak Brook 1976) (W. R. Cowell, ed.), Springer-Verlag, Berlin, 1977, pp. 452-483.

Ful80

L. W. Fullerton, A bibliography on the evaluation of mathematical functions, Computing Science Tech. Report No. 86, Bell Laboratories, Murray Hill, New Jersey 07974, 1980.

FW80

A. Fransén and S. Wrigge, High-precision values of the gamma function and of some related coefficients, Math. Comp. 34 (1980), 553-566, for addendum and corrigendum see same journal v. 37 (1981), pp. 233-235.

Gab79

B. Gabutti, On high precision methods for computing integrals involving Bessel functions, Math. Comp. 33 (1979), 1049-1057.

Gab80

B. Gabutti, On the generalization of a method for computing Bessel function integrals, J. Comput. Appl. Math. 6 (1980), 167-168.

Gaf88

P. W. Gaffney, When things go wrong $\ldots$, Pitman Research Notes in Mathematics Series (D. F. Griffiths and G. A. Watson, eds.), vol. 170, Longman Scientific and Technical, Harlow, Essex, U. K., 1988, pp. 67-114.

Gau64

W. Gautschi, Algorithm 222. Incomplete beta function ratios, Comm. ACM 7 (1964), 143-144, for certification see same journal v. 7 (1964), p. 244.

Gau65

W. Gautschi, Algorithm 259. Legendre functions for arguments larger than one, Comm. ACM 8 (1965), 488-492, for remark see ACM Trans. Math. Software, v. 3 (1977), pp. 204-205.

Gau69a

W. Gautschi, Algorithm 363. Complex error function, Comm. ACM 12 (1969), 635, for certification see same journal v. 15 (1972), pp. 465-466.

Gau69b

W. Gautschi, An application of minimal solutions of three-term recurrences to Coulomb wave functions, Aequationes Math. 2 (1969), 171-176.

Gau70

W. Gautschi, Efficient computation of the complex error function, SIAM J. Numer. Anal. 7 (1970), 187-198.

Gau73

W. Gautschi, Algorithm 471. Exponential integrals, Comm. ACM 16 (1973), 761-763.

Gau75

W. Gautschi, Computational methods in special functions--a survey, Theory and application of special functions, Proc. Advanced Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis., Academic Press, New York, 1975, pp. 1-98.

Gau77a

W. Gautschi, Algorithm 521. Repeated integrals of the coerror function, ACM Trans. Math. Software 3 (1977), 301-302.

Gau77b

W. Gautschi, Evaluation of the repeated integrals of the coerror function, ACM Trans. Math. Software 3 (1977), 240-252.

Gau79a

W. Gautschi, Algorithm 542. Incomplete gamma functions, ACM Trans. Math. Software 5 (1979), 482-489.

Gau79b

W. Gautschi, A computational procedure for incomplete gamma functions, ACM Trans. Math. Software 5 (1979), 466-481.

Gau82

W. Gautschi, On generating orthogonal polynomials, SIAM J. Sci. Statist. Comput. 3 (1982), 289-317.

Gau85

W. Gautschi, Orthogonal polynomials--constructive theory and applications, J. Comput. Appl. Math. 12/13 (1985), 61-76.

Gau90

W. Gautschi, Computational aspects of orthogonal polynomials, Orthogonal Polynomials: Theory and Practice (P. Nevai, ed.), Kluwer Academic Publishers, Dordrecht, 1990, NATO ASI Series, vol. C294, pp. 181-216.

Gau91a

W. Gautschi, Computational problems and applications of orthogonal polynomials, Orthogonal Polynomials and their Applications (C. Brezinski, L. Gori, and A. Ronveaux, eds.), J. C. Baltzer AG, Scientific Publishing Company, Basel, 1991, pp. 61-71.

Gau91b

W. Gautschi, On the paper ``A continued fraction approximation of the modified Bessel function ${I}_1(t)$'' by P. R. Parthasarathy and N. Balakrishnan, Appl. Math. Lett. 4 (1991), no. 5, 47-51.

Gau93a

W. Gautschi, Gauss-type quadrature rules for rational functions, International Series of Numerical Mathematics, vol. 112, Birkhäuser Verlag, Basel, 1993, pp. 111-130.

Gau93b

W. Gautschi, Is the recurrence relation for orthogonal polynomials always stable?, BIT 33 (1993), 277-284.

Gau93c

W. Gautschi, On the computation of generalized Fermi-Dirac and Bose-Einstein integrals, Comput. Phys. Comm. 74 (1993), 233-238.

Gau94

W. Gautschi, Algorithm 726. ORTHPOL--A package of routines for generating orthogonal polynomials and Gauss-type quadrature rules, ACM Trans. Math. Software 20 (1994), 21-62, for remark see same journal v. 24 (1998), p. 355.

Gau99

W. Gautschi, A note on the recursive calculation of incomplete gamma functions, ACM Trans. Math. Software 25 (1999), 101-107.

GB87

A. Ganguli and R. Baskaran, Generation of Bessel functions with complex arguments and integer orders, Internat. J. Comput. Math. 21 (1987), 43-64.

GH85

P. Griffiths and I. D. Hill (eds.), Applied statistics algorithms, Ellis Horwood Limited, Chichester, 1985.

GM81

B. Gabutti and B. Minetti, A new application of the discrete Laguerre polynomials in the numerical evaluation of the Hankel transform of a strongly decreasing even function, J. Comput. Phys. 42 (1981), 277-287.

Goa95

M. Goano, Algorithm 745. Computation of the complete and incomplete Fermi-Dirac integral, ACM Trans. Math. Software 21 (1995), 221-232, for remark see same journal v. 23 (1997), p. 295.

Gor69

R. G. Gordon, New method for constructing wavefunctions for bound states and scattering, J. Chem. Phys. 51 (1969), no. 1, 14-25.

GP64

I. Gargantini and T. Pomentale, Rational Chebyshev approximations to the Bessel function integrals $\operatorname{Ki}_{s}(x)$, Comm. ACM 7 (1964), 727-730.

GS78

W. Gautschi and J. Slavik, On the computation of modified Bessel function ratios, Math. Comp. 32 (1978), 865-875.

GS97

A. Gil and J. Segura, Evaluation of Legendre functions of argument greater than one, Comput. Phys. Comm. 105 (1997), no. 2-3, 273-283.

GS98

A. Gil and J. Segura, A code to evaluate prolate and oblate spheroidal harmonics, Comput. Phys. Comm. 108 (1998), 267-278.

GT81

R. Gastmans and W. Troost, On the evaluation of polylogarithmic integrals, Simon Stevin 55 (1981), 205-219.

Gue94

S. Gueron, Methods for fast computation of integral transforms, J. Computational Phys. 110 (1994), 164-170.

GZ75

E. S. Ginsberg and D. Zaborowski, Algorithm 490. The dilogarithm function of a real argument, Comm. ACM 18 (1975), 200-202, for remark see ACM Trans. Math. Software v. 2 (1976), p. 112.

GZ95

W. Gautschi and M. Zhang, Computing orthogonal polynomials in Sobolev spaces, Numer. Math. 71 (1995), 159-183.

Ham85

D. E. Hamilton, Remark on Algorithm 620: References and keywords for collected algorithms from ACM, ACM Trans. Math. Software 11 (1985), 305-307.

Han85

E. W. Hansen, Fast Hankel transform algorithm, IEEE Trans. Acoust. Speech Signal Process. 33 (1985), 666-671.

HCL+68

J. F. Hart, E. W. Cheney, C. L. Lawson, H. J. Maehly, C. K. Mesztenyi, J. R. Rice, H. C. Thacher, Jr., and C. Witzgall, Computer approximations, John Wiley and Sons, Inc., New York, 1968.

HD73

G. W. Hill and A. W. Davis, Algorithm 442. Normal deviate, Comm. ACM 16 (1973), 51-52.

Hea85

M. A. Heald, Rational approximations for the Fresnel integrals, Math. Comp. 44 (1985), 459-461.

Hem81

P. W. Hemker (ed.), NUMAL numerical procedures in Algol 60, Mathematisch Centrum Syllabus 47.1-7, Centrum voor Wiskunde en Informatica, Kruislaan 413, 1098 SJ, Amsterdam, 1981.

Hen79

P. Henrici, Zur numerischen Berechnung der Fresnelschen Integrale, Z. Angew. Math. Phys. 30 (1979), 209-219.

Hil70a

G. W. Hill, Algorithm 395. Student's $t$-distribution, Comm. ACM 13 (1970), 617-619, for remarks see ACM Trans. Math. Software v. 5 (1979), pp. 238-239, v. 7 (1981), pp. 247-249.

Hil70b

G. W. Hill, Algorithm 396. Student's $t$-quantiles, Comm. ACM 13 (1970), 619-620, for remarks see ACM Trans. Math. Software v. 5 (1979), pp. 238-239, v. 7 (1981), pp. 250-251.

Hil73

I. D. Hill, Algorithm AS 66. The normal integral, Appl. Statist. 22 (1973), 424-427.

Hil77

G. W. Hill, Algorithm 518. Incomplete Bessel function ${I}_{0}$: The von Mises distribution, ACM Trans. Math. Software 3 (1977), 279-284.

Hil81

G. W. Hill, Algorithm 571. Statistics for von Mises' and Fisher's distributions of directions: ${I}_1(x)/{I}_0(x), {I}_{1.5}(x)/{I}_{0.5}(x),$ and their inverses, ACM Trans. Math. Software 7 (1981), 233-238.

Hit68

S. Hitotumatu, On the numerical computation of Bessel functions through continued fraction, Comment. Math. Univ. St. Paul. 16 (1967/68), 89-113.

HM90a

T. R. Hopkins and D. R. Morse, Index of statistical algorithms, Appl. Statist. 39 (1990), 177-187.

HM90b

T. R. Hopkins and D. R. Morse, Remark on Algorithm 620: References and keywords for collected algorithms from ACM, ACM Trans. Math. Software 16 (1990), 401-403.

HN97a

M. Hiyama and H. Nakamura, Gaussian expansions of the two-center Coulomb functions, Comput. Phys. Comm. 103 (1997), 197-208.

HN97b

M. Hiyama and H. Nakamura, Two-center Coulomb functions, Comput. Phys. Comm. 103 (1997), 209-216.

Hod70

D. B. Hodge, Eigenvalues and eigenfunctions of the spheroidal wave equation, J. Math. Phys. 11 (1970), 2308-2312.

HR72

D. B. Hunter and T. Regan, A note on the evaluation of the complementary error function, Math. Comp. 26 (1972), 539-541.

Hsu93

Yupai P. Hsu, Development of a Gaussian hypergeometric function code in complex domains, Internat. J. Modern Phys. C 4 (1993), no. 4, 805-840.

Hum64

D. G. Hummer, Expansion of Dawson's function in a series of Chebyshev polynomials, Math. Comp. 18 (1964), 317-319.

Hun95

D. B. Hunter, The evaluation of Legendre functions of the second kind, Numer. Algorithms 10 (1995), 41-49.

IKF91

Y. Ikebe, Y. Kikuchi, and I. Fujishiro, Computing zeros and orders of Bessel functions, J. Comput. Appl. Math. 38 (1991), 169-184.

IKF+93

Yasuhiko Ikebe, Yasushi Kikuchi, Issei Fujishiro, Nobuyoshi Asai, Kouichi Takanashi, and Minoru Harada, The eigenvalue problem for infinite compact complex symmetric matrices with application to the numerical computation of complex zeros of ${J}\sb 0(z)-i{J}\sb 1(z)$ and of Bessel functions ${J}\sb m(z)$ of any real order $m$, Linear Algebra Appl. 194 (1993), 35-70.

IKJ95

M. Ikonomou, P. Köhler, and A. F. Jacob, Computation of integrals over the half-line involving products of Bessel functions, with application to microwave transmission lines, Z. Angew. Math. Mech. 75 (1995), no. 12, 917-926.

IMS91

MATH/LIBRARY special functions, version 2.0, Visual Numerics, Inc., 2500 Wilcrest Drive, Suite 200, Houston, Texas 77042, 1991, see also http://www.vni.com/.

Jab94

A. Jablonski, Numerical evaluation of spherical Bessel functions of the first kind, J. Computational Phys. 111 (1994), 256-259.

JE45

E. Jahnke and F. Emde, Tables of functions with formulae and curves, fourth ed., Dover Publications, Inc., New York, 1945.

JEL60

E. Jahnke, F. Emde, and F. Lösch, Tables of higher functions, sixth ed., McGraw-Hill, New York, 1960.

JL72

D. Jacobs and F. Lambert, On the numerical calculation of polylogarithms, BIT 12 (1972), 581-585.

Joh75

H. K. Johansen, An interactive computer/graphic-display-terminal system for interpretation of resistivity soundings, Geophys. Prospecting 23 (1975), 449-458.

JT80

W. B. Jones and W. J. Thron, Continued fractions: Analytic theory and applications, Encyclopedia of Mathematics and its Applications, vol. 11, Addison-Wesley Publishing Company, Reading, Massachusetts, 1980.

JT85

W. B. Jones and W. J. Thron, On the computation of incomplete gamma functions in the complex domain, J. Comput. Appl. Math. 12/13 (1985), 401-417.

Kae95

T. A. Kaeding, Pascal program for generating tables of SU(3) Clebsch-Gordan coefficients, Comput. Phys. Comm. 85 (1995), 82-88.

Kal92

S. L. Kalla, On the evaluation of the Gauss hypergeometric function, C. R. Acad. Bulgare Sci. 45 (1992), no. 6, 35-36.

Kar91

E. A. Karatsuba, Fast evaluation of transcendental functions, Problems Inform. Transmission 27 (1991), 339-360.

Kat78

C. R. Katholi, On the computation of values of the psi function from rapidly converging power series expansions, J. Statist. Comput. Simulation 8 (1978), 25-42.

KBH70

B. J. King, R. V. Baier, and S. Hanish, A Fortran computer program for calculating the prolate spheroidal radial functions of the first and second kind and their first derivatives, NRL Report No. 7012, Naval Res. Lab., Washington, D. C., 1970.

Ker80

M. K. Kerimov, Methods of computing the Riemann zeta-function and some generalizations of it, U.S.S.R. Comput. Math. and Math. Phys. 20 (1980), no. 6, 212-230.

KG80

W. J. Kennedy, Jr. and J. E. Gentle, Statistical computing, Marcel Dekker, New York, 1980.

Kha97

H. G. Khajah, Tau method approximation of the Gauss hypergeometric function, C. R. Acad. Bulgare Sci. 50 (1997), no. 6, 13-16.

Kin88

A. C. King, Periodic approximations to an elliptical function, Appl. Anal. 27 (1988), no. 4, 271-278.

KMR70

K. S. Kölbig, J. A. Mignaco, and E. Remiddi, On Nielsen's generalized polylogarithms and their numerical calculation, BIT 10 (1970), 38-73.

Köl72a

K. S. Kölbig, Programs for computing the logarithm of the gamma function, and the digamma function, for complex argument, Comput. Phys. Comm. 4 (1972), 221-226.

Köl72b

K. S. Kölbig, Remarks on the computation of Coulomb wavefunctions, Comput. Phys. Comm. 4 (1972), 214-220.

Köl81

K. S. Kölbig, A program for computing the conical functions of the first kind ${P}_{-\frac{1}{2} + i\tau}^m (x)$ for $m = 0$ and $m=1$, Comput. Phys. Comm. 23 (1981), 51-61.

Köl95

K. S. Kölbig, Chebyshev coefficients for the Clausen function ${Cl}_2(x)$, J. Comput. Appl. Math. 64 (1995), 295-297.

Kon96

E. Konishi, Calculation of complex polygamma functions, Sci. Rep. Hirosaki Univ. 43 (1996), 161-183.

Krä90

W. Krämer, Berechnung der Gammafunktion $\Gamma (x)$ für reelle Punkt- und Intervallargumente, Z. Angew. Math. Mech. 70 (1990), T581-T584.

Kro91

F. T. Krogh, ACM algorithms policy, ACM Trans. Math. Software 17 (1991), 427-430.

KRVZ98

P. Kravanja, O. Ragos, M. N. Vrahatis, and F. A. Zafiropoulos, ZEBEC: A mathematical software package for computing simple zeros of Bessel functions of real order and complex argument, Comput. Phys. Comm. 113 (1998), 220-238.

KS84a

M. K. Kerimov and S. L. Skorokhodov, Calculation of modified Bessel functions in the complex domain, U.S.S.R. Comput. Math. and Math. Phys. 24 (1984), no. 3, 15-24.

KS84b

M. K. Kerimov and S. L. Skorokhodov, Calculation of the complex zeros of the modified Bessel function of the second kind and its derivatives, U.S.S.R. Comput. Math. and Math. Phys. 24 (1984), no. 4, 115-123.

KS84c

M. K. Kerimov and S. L. Skorokhodov, Evaluation of complex zeros of Bessel functions ${J}_{\nu}(z)$ and ${I}_{\nu}(z)$ and their derivatives, U.S.S.R. Comput. Math. and Math. Phys. 24 (1984), no. 5, 131-141.

KS84d

K. S. Kölbig and B. Schorr, A program package for the Landau distribution, Comput. Phys. Comm. 31 (1984), 97-111.

KS85a

M. K. Kerimov and S. L. Skorokhodov, Calculation of the complex zeros of a Bessel function of the second kind and its derivatives, U.S.S.R. Comput. Math. and Math. Phys. 25 (1985), no. 5, 117-128.

KS85b

M. K. Kerimov and S. L. Skorokhodov, Calculation of the complex zeros of Hankel functions and their derivatives, U.S.S.R. Comput. Math. and Math. Phys. 25 (1985), no. 6, 26-36.

KS85c

M. K. Kerimov and S. L. Skorokhodov, Calculation of the multiple zeros of the derivatives of the cylindrical Bessel functions ${J}_{\nu}(z)$ and ${Y}_{\nu}(z)$, U.S.S.R. Comput. Math. and Math. Phys. 25 (1985), no. 6, 101-107.

KS87

M. K. Kerimov and S. L. Skorokhodov, On the calculation of the multiple complex roots of the derivatives of cylindrical Bessel functions, U.S.S.R. Comput. Math. and Math. Phys. 27 (1987), no. 6, 18-25.

Kuk71

H. Kuki, Mathematical function subprograms for basic system libraries-- objectives, constraints and trade-off, Mathematical Software (J. R. Rice, ed.), Academic Press, New York, 1971, pp. 187-199.

Kuk72a

H. Kuki, Algorithm 421. Complex gamma function with error control, Comm. ACM 15 (1972), 271-272.

Kuk72b

H. Kuki, Complex gamma function with error control, Comm. ACM 15 (1972), 262-267.

KvB70

B. J. King and A. L. van Buren, A Fortran computer program for calculating the prolate and oblate angle functions of the first kind and their first and second derivatives, NRL Report No. 7161, Naval Res. Lab., Washington, D. C., 1970.

LCY65

L. A. Lyusternik, O. A. Chervonenkis, and A. R. Yanpol'skii, Handbook for computing elementary functions, International Series of Monographs in Pure and Applied Mathematics, vol. 76, Pergamon Press, Oxford, 1965.

LDP93

Y. Li, X. Dong, and S. Pan, Computation of auxiliary functions in STO molecular integrals up to arbitrary accuracy. I. Evaluation of incomplete gamma function ${E}_n(x)$ by forward recursion, Internat. J. Quantum Chem. 45 (1993), 3-14.

Lee79

W. R. Leeb, Algorithm 537. Characteristic values of Mathieu's differential equation, ACM Trans. Math. Software 5 (1979), 112-117.

Lee80

S.-Y. Lee, The inhomogeneous Airy functions $\operatorname{Gi}(z)$ and $\operatorname{Hi}(z)$, J. Chem. Phys. 72 (1980), 332-336.

Lee90

D. K. Lee, Application of theta functions for numerical evaluation of complete elliptic integrals of the first and second kinds, Comput. Phys. Comm. 60 (1990), 319-327.

Lee92

D. K. Lee, Calculation of coefficients in a power-series expansion of the nome $q = \exp[-\pi{K}(k')/{K}(k)]$, Comput. Phys. Comm. 70 (1992), 292-296.

Lem97

D. Lemoine, Optimal cylindrical and spherical Bessel transforms satisfying bound state boundary conditions, Comput. Phys. Comm. 99 (1997), 297-306.

Let96

Frank G. Lether, Rational approximation formulas for computing the positive zeros of ${J}\sb 0(x)$, J. Comput. Appl. Math. 67 (1996), no. 1, 167-172.

Let97

Frank G. Lether, Constrained near-minimax rational approximations to Dawson's integral, Appl. Math. Comput. 88 (1997), no. 2-3, 267-274.

Let98

Frank G. Lether, Shifted rectangular quadrature rule approximations to Dawson's integral ${F}(x)$, J. Comput. Appl. Math. 92 (1998), no. 2, 97-102.

Lev69

D. A. Levine, Algorithm 344. Student's $t$-distribution, Comm. ACM 12 (1969), 37-38, for remarks see same journal v. 13 (1970), pp. 124 and 449.

Lew91

S. Lewanowicz, Evaluation of Bessel function integrals with algebraic singularities, J. Comput. Appl. Math. 37 (1991), 101-112.

LF94

Albrecht Lindner and Heino Freese, A new method to compute Mathieu functions, J. Phys. A 27 (1994), no. 16, 5565-5571.

LG64

H. Lotsch and M. Gray, Algorithm 244. Fresnel integrals, Comm. ACM 7 (1964), 660-661.

Lin72

P. Linz, A method for computing Bessel function integrals, Math. Comp. 26 (1972), 509-513.

Liu96

K. M. Liu, Numerical solution of Mathieu's differential equation with the tau method, Southeast Asian Bull. Math. 20 (1996), no. 3, 59-63, Conference on Scientific Computation '94 (Shatin, 1994).

LK73

P. Linz and T. E. Kropp, A note on the computation of integrals involving products of trigonometric and Bessel functions, Math. Comp. 27 (1973), 871-872.

LMS73a

D. W. Lozier, L. C. Maximon, and W. L. Sadowski, A bit comparison program for algorithm testing, Comput. J. 16 (1973), 111-117.

LMS73b

D. W. Lozier, L. C. Maximon, and W. L. Sadowski, Performance testing of a Fortran library of mathematical function routines--A case study in the application of testing techniques, J. Res. Nat. Bur. Standards 77B (1973), 101-110.

LO93

D. W. Lozier and F. W. J. Olver, Airy and Bessel functions by parallel integration of ODEs, Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing, vol. 2 (R. F. Sincovec, D. E. Keyes, M. R. Leuze, L. R. Petzold, and D. A. Reed, eds.), Society for Industrial and Applied Mathematics, Philadelphia, 1993, pp. 531-538.

LO94

D. W. Lozier and F. W. J. Olver, Numerical evaluation of special functions, Mathematics of Computation 1943-1993: A Half-Century of Computational Mathematics (W. Gautschi, ed.), Proceedings of Symposia in Applied Mathematics, vol. 48, American Mathematical Society, Providence, Rhode Island 02940, 1994, pp. 79-125. See also http://math.nist.gov/nesf/.

LPM81

A. R. Lehman, W. C. Parke, and L. C. Maximon, Numerical evaluation of integrals containing a spherical Bessel function by product integration, J. Math. Phys. 22 (1981), 1399-1413.

LPT80

M. C. Lorenzini, G. Puleo, and A. Tortorici Macaluso, Un package di aritmetica in multiprecisione ed applicazione al calcolo dei polinomi di Jacobi, Hermite, Laguerre, Legendre, Chebyshev, Atti Accad. Sci. Lett. Arti Palermo Ser. 4, Parte 1 39 (1980), 339-376.

LR74

W. P. Latham and R. W. Redding, On the calculation of the parabolic cylinder functions, J. Comput. Phys. 16 (1974), 66-75.

LS81

D. W. Lozier and J. M. Smith, Algorithm 567. Extended-range arithmetic and normalized Legendre polynomials, ACM Trans. Math. Software 7 (1981), 141-146.

LS91

A. I. Litvin and S. D. Simonzhenkov, Computation of Fermi-Dirac functions, Comput. Math. Math. Phys. 31 (1991), no. 8, 100-103.

LS95

S. K. Lucas and H. A. Stone, Evaluating infinite integrals involving Bessel functions of arbitrary order, J. Comput. Appl. Math. 64 (1995), 217-231.

Luc95

S. K. Lucas, Evaluating infinite integrals involving products of Bessel functions of arbitrary order, J. Comput. Appl. Math. 64 (1995), 269-282.

Luk68

Y. L. Luke, Approximations for elliptic integrals, Math. Comp. 22 (1968), 627-634.

Luk69a

Y. L. Luke, The special functions and their approximations, vol. 1, Academic Press, New York, 1969.

Luk69b

Y. L. Luke, The special functions and their approximations, vol. 2, Academic Press, New York, 1969.

Luk70a

Y. L. Luke, Evaluation of the gamma function by means of Padé approximations, SIAM J. Math. Anal. 1 (1970), 266-281.

Luk70b

Y. L. Luke, Further approximations for elliptic integrals, Math. Comp. 24 (1970), 191-198.

Luk71a

Y. L. Luke, Miniaturized tables of Bessel functions, Math. Comp. 25 (1971), 323-330.

Luk71b

Y. L. Luke, Miniaturized tables of Bessel functions. II, Math. Comp. 25 (1971), 789-795, for corrigendum see same journal v. 26 (1972), Microfiche Supplement A1-A7.

Luk72a

Y. L. Luke, Miniaturized tables of Bessel functions. III, Math. Comp. 26 (1972), 237-240, with Microfiche Supplement.

Luk72b

Y. L. Luke, On generating Bessel functions by use of the backward recurrence formula, Tech. Report ARL 72-0030, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio, 1972.

Luk75

Y. L. Luke, Mathematical functions and their approximations, Academic Press, New York, 1975.

Luk76

Y. L. Luke, On the expansion of exponential type integrals in series of Chebyshev polynomials, Theory of Approximation with Applications (A. G. Law and B. N. Sahney, eds.), Academic Press, Inc., New York, 1976, pp. 180-199.

Luk77a

Y. L. Luke, Algorithms for rational approximations for a confluent hypergeometric function, Utilitas Math. 11 (1977), 123-151.

Luk77b

Y. L. Luke, Algorithms for the computation of mathematical functions, Academic Press, New York, 1977.

Lun85

J. Lund, Bessel transforms and rational extrapolation, Numer. Math. 47 (1985), 1-14.

LW90

F. G. Lether and P. R. Wenston, An algorithm for the numerical computation of the Voigt function, Appl. Math. Comput. 35 (1990), 277-289.

LW91

F. G. Lether and P. R. Wenston, The numerical computation of the Voigt function by a corrected midpoint quadrature rule for $(-\infty,\infty)$, J. Comput. Appl. Math. 34 (1991), 75-92.

LW95

F. G. Lether and P. R. Wenston, Minimax approximations to the zeros of ${P}_n(x)$ and Gauss-Legendre quadrature, J. Comput. Appl. Math. 59 (1995), 245-252.

LY88

T. Y. Lemczyk and M. M. Yovanovich, Efficient evaluation of incomplete elliptic integrals and functions, Comput. Math. Appl. 16 (1988), 747-757.

Lyn93

A. E. Lynas-Gray, VOIGTL--A fast subroutine for Voigt function evaluation on vector processors, Comput. Phys. Comm. 75 (1993), 135-142.

Mac89

A. J. MacLeod, Algorithm AS 245. A robust and reliable algorithm for the logarithm of the gamma function, Appl. Statist. 38 (1989), 397-402.

Mac93

A. J. MacLeod, Chebyshev expansions for modified Struve and related functions, Math. Comp. 60 (1993), 735-747.

Mac94a

Allan J. MacLeod, Computation of inhomogeneous Airy functions, J. Comput. Appl. Math. 53 (1994), no. 1, 109-116.

Mac94b

Allan J. MacLeod, Table-based tests for Bessel function software, Adv. Comput. Math. 2 (1994), no. 2, 251-260.

Mac96a

A. J. MacLeod, Algorithm 757: MISCFUN, a software package to compute uncommon special functions, ACM Trans. Math. Software 22 (1996), 288-301.

Mac96b

A. J. MacLeod, Rational approximations, software and test methods for sine and cosine integrals, Numer. Algorithms 12 (1996), 259-272.

Mac97

D. A. MacDonald, On the computation of zeroes of ${J}\sb n(z)-i{J}\sb {n+1}(z)=0$, Quart. Appl. Math. 55 (1997), no. 4, 623-633.

Mac98

A. J. MacLeod, Algorithm 779. Fermi-Dirac functions of order $-1/2$, $1/2$, $3/2$, $5/$2, ACM Trans. Math. Software 24 (1998), 1-12.

Mar65

B. Markman, Contribution no. 14. The Riemann zeta function, BIT 5 (1965), 138-141.

Mar82

A. L. Marshak, On the approximation of the exponential integral by quadrature formulae, U.S.S.R. Comput. Math. and Math. Phys. 22 (1982), no. 5, 20-28.

Mas83

J. P. Mason, Cylindrical Bessel functions for a large range of complex arguments, Comput. Phys. Comm. 30 (1983), 1-11.

Mat92

MATLAB high performance numeric computation and visualization software reference guide, The MathWorks, Inc., Cochituate Place, 24 Prime Park Way, Natick, Massachusetts 01760, August 1992, electronic mail address is info@@mathworks.com.

Mat93a

Mathcad 4.0 user's guide, MathSoft Inc., 201 Broadway, Cambridge, Massachusetts 02139, March 1993.

Mat93b

Gregory Matviyenko, On the evaluation of Bessel functions, Appl. Comput. Harmon. Anal. 1 (1993), no. 1, 116-135.

MB73a

K. L. Majumder and G. P. Bhattacharjee, Algorithm AS 63. The incomplete beta integral, Appl. Statist. 22 (1973), 409-411, for remark see same journal v. 26 (1977), pp. 111-114.

MB73b

K. L. Majumder and G. P. Bhattacharjee, Algorithm AS 64. Inverse of the incomplete beta function ratio, Appl. Statist. 22 (1973), 411-414, for remarks and corrections see same journal v. 26 (1977), pp. 111-114, v. 39 (1990), pp. 309-310, v. 40 (1991), p. 236.

MBF94

P. Marksteiner, E. Badralexe, and A. J. Freeman, Neumann-type expansion of Coulomb functions, J. Computational Phys. 111 (1994), 49-52.

McC74

J. H. McCabe, A continued fraction expansion, with a truncation error estimate, for Dawson's integral, Math. Comp. 28 (1974), 811-816.

McC81

P. McCullagh, A rapidly convergent series for computing $\psi (z)$ and its derivatives, Math. Comp. 36 (1981), 247-248.

MDS92

R. C. McPhedran, D. H. Dawes, and T. C. Scott, On a Bessel function integral, Appl. Algebra Engrg. Comm. Comput. 2 (1992), no. 3, 207-216.

MF86

V. P. Modenov and A. V. Filonov, Calculation of zeros of cylindrical functions and their derivatives, Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet. (1986), no. 2, 63-64, 71 (Russian).

MF94

K. Mayrhofer and F. D. Fischer, Analytical solutions and a numerical algorithm for the Gauss's hypergeometric function $\sb 2{F}\sb 1(a,b;c;z)$, Z. Angew. Math. Mech. 74 (1994), no. 7, 265-273.

MH73

T. Morita and T. Horiguchi, Convergence of arithmetic-geometric mean procedure for the complex variables and the calculation of the complete elliptic integrals with complex modulus, Numer. Math. 20 (1973), 425-430, for correction see same journal v. 29 (1978), pp. 233-236.

Mid75

P. Midy, An improved calculation of the general elliptic integral of the second kind in the neighbourhood of $x=0$, Numer. Math. 25 (1975), 99-101.

MM90

P. Maliký and M. Maliká, On the computation of Riccati-Bessel functions, Apl. Mat. 35 (1990), 487-493.

MMV81

G. Maino, E. Menapace, and A. Ventura, Computation of parabolic cylinder functions by means of a Tricomi expansion, J. Comput. Phys. 40 (1981), 294-304.

MN97

N. Mohankumar and A. Natarajan, The accurate evaluation of a particular Fermi-Dirac integral, Comput. Phys. Comm. 101 (1997), 47-53.

Moi88

A. I. Moiseyev, Computation of certain functions related to the Hurwitz zeta-function, U.S.S.R. Comput. Math. and Math. Phys. 28 (1988), no. 3, 1-6.

Moo81

W. Moon, Airy function with complex arguments, Comput. Phys. Comm. 22 (1981), 411-417.

Moo82

R. J. Moore, Algorithm AS 187. Derivatives of the incomplete gamma integral, Appl. Statist. 31 (1982), 330-335.

Moo83

D. R. Mook, An algorithm for the numerical evaluation of the Hankel and Abel transforms, IEEE Trans. Acoust. Speech Signal Process. 31 (1983), 979-985.

Mor69

J. Morris, Algorithm 346. $F$-test probabilities, Comm. ACM 12 (1969), 184-185, for remark see ACM Trans. Math. Software v. 14 (1988), pp. 288-289.

Mor79

R. Morris, The dilogarithm function of a real argument, Math. Comp. 33 (1979), 778-787.

Mor80

M. Mori, Analytic representations suitable for numerical computation of some special functions, Numer. Math. 35 (1980), 163-174.

Mor83

M. Mori, A method for evaluation of the error function of real and complex variable with high relative accuracy, Publ. Res. Inst. Math. Sci. 19 (1983), 1081-1094.

Mor93

A. H. Morris, Jr., NSWC library of mathematics subroutines, NSWCDD/TR-92/425, Naval Surface Warfare Center, Dahlgren Division, Dahlgren, Virginia, 22448, January 1993.

Mor96

Tohru Morita, Use of the Gauss contiguous relations in computing the hypergeometric functions ${F}(n+1/2,n+1/2; m; z)$, Interdiscip. Inform. Sci. 2 (1996), no. 1, 63-74.

Mor99

T. Morita, Calculation of the elliptic integrals of the first and second kinds with complex modulus, Numer. Math. 82 (1999), 677-688.

MOS66

W. Magnus, F. Oberhettinger, and R. P. Soni, Formulas and theorems for the special functions of mathematical physics, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, vol. 52, Springer-Verlag, New York, 1966.

Mos89

S. L. B. Moshier, Methods and programs for mathematical functions, Ellis Horwood Limited, Chichester, 1989, separate diskette. Programs downloadable from Netlib and GAMS.

MR71

F. Matta and A. Reichel, Uniform computation of the error function and other related functions, Math. Comp. 25 (1971), 339-344.

MY91

P. Midy and Y. Yakovlev, Computing some elementary functions of a complex variable, Math. Comput. Simulation 33 (1991), 33-49.

NAG99

NAG Fortran library manual, mark 19, vol. 10, NAG Inc., 1400 Opus Place, Suite 200, Downers Grove, Illinois 60515-5702, June 1999.

NC66

W. J. Nellis and B. C. Carlson, Reduction and evaluation of elliptic integrals, Math. Comp. 20 (1966), 223-231.

NDT69

E. W. Ng, C. J. Devine, and R. F. Tooper, Chebyshev polynomial expansion of Bose-Einstein functions of orders 1 to 10, Math. Comp. 23 (1969), 639-643.

Ném65

G. Németh, Chebyshev expansions for Fresnel Integrals, Numer. Math. 7 (1965), 310-312.

Ném92

G. Németh, Mathematical approximation of special functions: Ten papers on Chebyshev expansions, Nova Science Publishers Inc., Commack, NY, 1992.

Nes84

R. K. Nesbet, Algorithms for regular and irregular Coulomb and Bessel functions, Comput. Phys. Comm. 32 (1984), 341-347.

New84

J. N. Newman, Approximations for the Bessel and Struve functions, Math. Comp. 43 (1984), 551-556.

Ng75

E. W. Ng, A comparison of computational methods and algorithms for the complex gamma function, ACM Trans. Math. Software 1 (1975), 56-70.

NM93

A. Natarajan and N. Mohan Kumar, On the numerical evaluation of the generalised Fermi-Dirac integrals, Comput. Phys. Comm. 76 (1993), 48-50.

NPB92a

M. Nardin, W. F. Perger, and A. Bhalla, Algorithm 707. CONHYP: A numerical evaluator of the confluent hypergeometric function for complex arguments of large magnitudes, ACM Trans. Math. Software 18 (1992), 345-349.

NPB92b

M. Nardin, W. F. Perger, and A. Bhalla, Numerical evaluation of the confluent hypergeometric function for complex arguments of large magnitudes, J. Comput. Appl. Math. 39 (1992), 193-200.

NT84

C. J. Noble and I. J. Thompson, COULN, a program for evaluating negative energy Coulomb functions, Comput. Phys. Comm. 33 (1984), 413-419.

OFM78

A. V. Oppenheim, G. V. Frisk, and D. R. Martinez, An algorithm for the numerical evaluation of the Hankel transform, Proc. Inst. Electr. Electron. Engrg. 66 (1978), 264-265.

Olv74

F. W. J. Olver, Asymptotics and special functions, Academic Press, New York, 1974.

Olv91

F. W. J. Olver, Review of United Laboratories, Inc., Mathematical Function Library for Microsoft-Fortran, Wiley, New York, 1989, Math. Comp. 56 (1991), 879-885.

OM68

D. Osborn and R. Madey, The incomplete beta function and its ratio to the complete beta function, Math. Comp. 22 (1968), 159-162.

Öpi87

U. Öpik, A program to set up systems of orthogonal polynomials, Comput. Phys. Comm. 46 (1987), 263-296.

OPP95

C. Osácar, J. Palacián, and M. Palacios, Numerical evaluation of the dilogarithm of complex argument, Celestial Mech. Dynam. Astronom. 62 (1995), no. 1, 93-98.

OS72

F. W. J. Olver and D. J. Sookne, Note on backward recurrence algorithms, Math. Comp. 26 (1972), 941-947.

OS83

F. W. J. Olver and J. M. Smith, Associated Legendre functions on the cut, J. Comput. Phys. 51 (1983), 502-518.

PA92

C. U. Pabon-Ortiz and M. Artoni, Laguerre polynomials: Novel properties and numerical generation scheme for analysis of a discrete probability distribution, Comput. Phys. Comm. 71 (1992), 215-221.

PA99

A. Poquérusse and S. Alexiou, Fast analytic formulas for the modified Bessel functions of imaginary order for spectral line broadening calculations, J. Quant. Spectr. Rad. Trans. 62 (1999), 389-395.

Pac70

K. A. Paciorek, Algorithm 385. Exponential integral $\operatorname{Ei}(x)$, Comm. ACM 13 (1970), 446-447, for certification and remarks see same journal v. 13 (1970), pp. 448-449 and p. 750; v. 15 (1972), p. 1074.

Pal69

A. A. Pal'cev, The computation of spheroidal functions and their first derivatives on a computer. I, Vesc Akad. Navuk BSSR Ser. Fz.-Mat. Navuk (1969), no. 1, 19-25 (Russian).

Pas88

S. Paszkowski, Evaluation of Fermi-Dirac integral, Nonlinear Numerical Methods and Rational Approximation (A. Cuyt, ed.), D. Reidel Publishing Company, Dordrecht, 1988, pp. 435-444.

Pas91

S. Paszkowski, Evaluation of the Fermi-Dirac integral of half-integer order, Zastos. Mat. 21 (1991), 289-301.

Pas95

S. Paszkowski, Quasipower and hypergeometric series--construction and evaluation, Numer. Algorithms 10 (1995), 337-361.

PB72

R. Piessens and M. Branders, Chebyshev polynomial expansions of the Riemann zeta function, Math. Comp. 26 (1972), 1022.

PB82

R. Piessens and M. Branders, Approximation for Bessel functions and their application in the computation of Hankel transforms, Comput. Math. Appl. 8 (1982), 305-311.

PB83

R. Piessens and M. Branders, Modified Clenshaw-Curtis method for the computation of Bessel function integrals, BIT 23 (1983), 370-381.

PB84

R. Piessens and M. Branders, Algorithm 28. Algorithm for the computation of Bessel function integrals, J. Comput. Appl. Math. 11 (1984), 119-137.

PB85

R. Piessens and M. Branders, A survey of numerical methods for the computation of Bessel function integrals, Rend. Sem. Mat. Univ. Politec. Torino Fascicolo Speciale. Special Functions: Theory and Computation (1985), 249-265.

PBN93

W. F. Perger, A. Bhalla, and M. Nardin, A numerical evaluator for the generalized hypergeometric series, Comput. Phys. Comm. 77 (1993), 249-254.

PDK96

S. D. Panteliou, A. D. Dimarogonas, and I. N. Katz, Direct and inverse interpolation for Jacobian elliptic functions, zeta function of Jacobi and complete elliptic integrals of the second kind, Comput. Math. Appl. 32 (1996), no. 8, 51-57.

PDL93

Brian A. Pettitt, Werner Danchura, and Donna Labun, Spherical Bessel transforms, J. Comput. Phys. 105 (1993), no. 1, 178-181.

Pea22

K. Pearson, Tables of the incomplete ${\Gamma}$-function, H. M. Stationery Office, London, 1922, reissued by Biometrika, 1934.

Pex70

R. L. Pexton, Computer investigation of Coulomb wave functions, Math. Comp. 24 (1970), 409-411.

Phi88

H. N. Phien, A Fortran routine for the computation of gamma percentiles, Adv. Eng. Software 10 (1988), 159-164.

Phi90

H. N. Phien, A note on the computation of the incomplete beta function, Adv. Eng. Software 12 (1990), 39-44.

Pic89

B. Pichon, Numerical calculation of the generalized Fermi-Dirac integrals, Comput. Phys. Comm. 55 (1989), 127-136.

Pie82

R. Piessens, Automatic computation of Bessel function integrals, Comput. Phys. Comm. 25 (1982), 289-295.

Pie84a

R. Piessens, Chebyshev series approximations for the zeros of the Bessel functions, J. Comput. Phys. 53 (1984), 188-192.

Pie84b

R. Piessens, The computation of Bessel functions on a small computer, Comput. Math. Appl. 10 (1984), 161-166.

Pie90

R. Piessens, On the computation of zeros and turning points of Bessel functions, Bull. Soc. Math. Grèce (N.S.) 31 (1990), 117-122.

Pri75

P. J. Prince, Algorithm 498. Airy functions using Chebyshev series approximations, ACM Trans. Math. Software 1 (1975), 372-379.

PT84

B. A. Popov and G. S. Tesler, Computation of functions on electronic computers--handbook, Naukova Dumka, Kiev, 1984 (Russian), see review by K. S. Kölbig in Math. Comp. v. 55 (1990), pp. 395-397.

PT90

W. H. Press and S. A. Teukolsky, Elliptic integrals, Comput. in Phys. 4 (1990), Jan/Feb, 92-96.

PTVF92

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical recipes in Fortran 77. The art of scientific computing, second ed., Cambridge University Press, 1992., Reprinted with corrections in 1997. Diskettes and example books available. Editions exist in Basic (1991), C (1992), Fortran (1992), Macintosh Fortran (1988) and Pascal (1989).

Puo88

M. Puoskari, A method for computing Bessel function integrals, J. Comput. Phys. 75 (1988), 334-344.

PW90a

G. P. M. Poppe and C. M. J. Wijers, Algorithm 680. Evaluation of the complex error function, ACM Trans. Math. Software 16 (1990), 47.

PW90b

G. P. M. Poppe and C. M. J. Wijers, More efficient computation of the complex error function, ACM Trans. Math. Software 16 (1990), 38-46.

RBMW59

M. Rotenberg, R. Bivins, N. Metropolis, and J. K. Wooten, Jr., The 3-j and 6-j symbols, The Technology Press, Massachusetts Institute of Technology, Cambridge, Massachusetts, 1959.

Rem73

G. F. Remenets, Computation of Hankel (Bessel) functions of complex index and argument by numerical integration of a Schläfli contour integral, U.S.S.R. Comput. Math. and Math. Phys. 13 (1973), no. 6, 58-67.

Ren96

O. Renault, A new algorithm for computing orthogonal polynomials, J. Comput. Appl. Math. 75 (1996), 231-248.

RF93

Yu. L. Ratis and P. Fernández de Córdoba, A code to calculate (high order) Bessel functions based on the continued fractions method, Comput. Phys. Comm. 76 (1993), 381-388.

RH84

J. R. Rice and R. J. Hanson, Algorithm 620. References and keywords for collected algorithms from ACM, ACM Trans. Math. Software 10 (1984), 359-360.

Ric83

J. R. Rice, Numerical methods, software and analysis: IMSL reference edition, McGraw-Hill Book Company, New York, 1983.

Riv90

T. J. Rivlin, Chebyshev polynomials. From approximation theory to algebra and number theory, second ed., John Wiley and Sons, Inc., New York, 1990.

RL76

R. W. Redding and W. P. Latham, On the calculation of the parabolic cylinder functions. II. The function ${V}(a,x)$, J. Comput. Phys. 20 (1976), 256-258.

RL80

S. R. Rengarajan and J. E. Lewis, Mathieu functions of integral orders and real arguments, IEEE Trans. Microwave Theory Tech. 28 (1980), 276-277.

RP96

V. Mohammad Raffee and C. L. Parihar, Computational method for the hypergeometric function $\sb 3{F}\sb 2(a,b,c;d,e;z)$, J. Maulana Azad College Tech. 29 (1996), 87-99.

RS81

M. Razaz and J. L. Schonfelder, Remark on Algorithm 498. Airy functions using Chebyshev series approximations, ACM Trans. Math. Software 7 (1981), 404-405.

RWGH87

J. P. Royston, J. B. Webb, P. Griffiths, and I. D. Hill, The construction and description of algorithms, Appl. Statist. 36 (1987), 94-103.

Ryb89

G. B. Rybicki, Dawson's integral and the sampling theorem, Comput. in Phys. 3 (1989), Mar/Apr, 85-87.

SAG79

Z. Schulten, D. G. M. Anderson, and R. G. Gordon, An algorithm for the evaluation of the complex Airy functions, J. Comput. Phys. 31 (1979), 60-75.

Sag91a

R. P. Sagar, A Gaussian quadrature for the calculation of generalized Fermi-Dirac integrals, Comput. Phys. Comm. 66 (1991), 271-275.

Sag91b

R. P. Sagar, On the evaluation of the Fermi-Dirac integrals, Astrophys. J. 376 (1991), 364-366.

Sal89

K. L. Sala, Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean, SIAM J. Math. Anal. 20 (1989), 1514-1528.

SBK92

O. A. Sharafeddin, H. F. Bowen, and D. J. Kouri, Numerical evaluation of spherical Bessel transforms via fast Fourier transforms, J. Comput. Phys. 100 (1992), 294-296.

Sch74

B. Schorr, Programs for the Landau and the Vavilov distributions and the corresponding random numbers, Comput. Phys. Comm. 7 (1974), 215-224.

Sch76

J. L. Schonfelder, The production of special function routines for a multi-machine library, Software--Practice and Experience 6 (1976), 71-82.

Sch78

J. L. Schonfelder, Chebyshev expansions for the error and related functions, Math. Comp. 32 (1978), 1232-1240.

Sea82

M. J. Seaton, Coulomb functions analytic in the energy, Comput. Phys. Comm. 25 (1982), 87-95.

Sec99

J. D. Secada, Numerical evaluation of the Hankel transform, Comput. Phys. Comm. 116 (1999), 278-294.

Seg98

J. Segura, A global Newton method for the zeros of cylinder functions, Numer. Algorithms 18 (1998), 259-276.

SFR97

J. Segura, P. Fernández de Córdoba, and Yu. L. Ratis, A code to evaluate modified Bessel functions based on the continued fraction method, Comput. Phys. Comm. 105 (1997), no. 2-3, 263-272.

SG72

A. J. Strecok and J. A. Gregory, High precision evaluation of the irregular Coulomb wave functions, Math. Comp. 26 (1972), 955-961.

SG98

J. Segura and A. Gil, Parabolic cylinder functions of integer and half-integer orders for nonnegative arguments, Comput. Phys. Comm. 115 (1998), 69-86.

SGA81

Z. Schulten, R. G. Gordon, and D. G. M. Anderson, A numerical algorithm for the evaluation of Weber parabolic cylinder functions ${U}(a,x), {V}(a,x)$, and ${W}(a,\pm x)$, J. Comput. Phys. 42 (1981), 213-237.

She74

V. B. Sheorey, Chebyshev expansions for wave functions, Comput. Phys. Comm. 7 (1974), 1-12.

She88

B. L. Shea, Algorithm AS 239. Chi-squared and incomplete gamma integral, Appl. Statist. 37 (1988), 466-473.

Shi93a

R. B. Shirts, Algorithm 721. MTIEU1 and MTIEU2: Two subroutines to compute eigenvalues and solutions to Mathieu's differential equation for noninteger and integer order, ACM Trans. Math. Software 19 (1993), 391-406.

Shi93b

R. B. Shirts, The computation of eigenvalues and solutions of Mathieu's differential equation for noninteger order, ACM Trans. Math. Software 19 (1993), 377-390.

Sid97

A. Sidi, Computation of infinite integrals involving Bessel functions of arbitrary order by the $\overline {D}$-transformation, J. Comput. Appl. Math. 78 (1997), 125-130.

Sie77

A. E. Siegman, Quasi fast Hankel transform, Optics Lett. 1 (1977), 13-15.

Sim64

J. M. S. Simões Pereira, Algorithm 234. Poisson-Charlier polynomials, Comm. ACM 7 (1964), 420, for certification see same journal v. 8 (1965), p. 105.

SJ96

P. N. Shivakumar and Chuanxiang Ji, Upper and lower bounds for inverse elements of finite and infinite tridiagonal matrices, Linear Algebra Appl. 247 (1996), 297-316.

Sko85

S. L. Skorokhodov, On the computation of complex zeros of the modified Bessel function of the second kind, Soviet Math. Dokl. 31 (1985), 78-81.

SL73

W. L. Sadowski and D. W. Lozier, A unified standards approach to algorithm testing, Program Test Methods (W. C. Hetzel, ed.), Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1973, pp. 277-290.

SL81

M. M. Shepherd and J. G. Laframboise, Chebyshev approximation of
$(1+2x)\operatorname{exp}(x^2)\operatorname{erfc} x$ in $0\le x < \infty$, Math. Comp. 36 (1981), 249-253.

SM75

B. P. Sinha and R. H. MacPhie, On the computation of the prolate spheroidal radial functions of the second kind, J. Math. Phys. 16 (1975), 2378-2381.

Smi89

D. M. Smith, Efficient multiple-precision evaluation of elementary functions, Math. Comp. 52 (1989), 131-134.

Smi91

D. M. Smith, Algorithm 693. A Fortran package for floating-point multiple-precision arithmetic, ACM Trans. Math. Software 17 (1991), 273-283.

Sny93

W. V. Snyder, Algorithm 723. Fresnel integrals, ACM Trans. Math. Software 19 (1993), 452-456, for remark see same journal v. 22 (1996), pp. 498-500.

SO87

J. Spanier and K. B. Oldham, An atlas of functions, Hemisphere Publishing Corporation, Washington, D. C., 1987.

SOL81

J. M. Smith, F. W. J. Olver, and D. W. Lozier, Extended-range arithmetic and normalized Legendre polynomials, ACM Trans. Math. Software 7 (1981), 93-105.

SP75

P. Spellucci and P. Pulay, Effective calculation of the incomplete gamma function for parameter values $\alpha = (2n+1)/2,n=0,\dots,5$, Angew. Informatik 17 (1975), 30-32.

Spo94

John L. Spouge, Computation of the gamma, digamma, and trigamma functions, SIAM J. Numer. Anal. 31 (1994), no. 3, 931-944.

Spr91

J. C. Sprott, Numerical recipes: Routines and examples in BASIC, Cambridge University Press, 1991.

Str68

A. J. Strecok, On the calculation of the inverse of the error function, Math. Comp. 22 (1968), 144-158.

Sym92

MACSYMA reference manual, version 13, Symbolics, Inc., 20 Academy St., Arlington, Massachusetts 02174-6436, November 1992.

SZ70

I. A. Stegun and R. Zucker, Automatic computing methods for special functions, J. Res. Nat. Bur. Standards 74B (1970), 211-224.

SZ74

I. A. Stegun and R. Zucker, Automatic computing methods for special functions. Part II. The exponential integral ${E}_n(x)$, J. Res. Nat. Bur. Standards 78B (1974), 199-216.

SZ76

I. A. Stegun and R. Zucker, Automatic computing methods for special functions. Part III. The sine, cosine, exponential integrals, and related functions, J. Res. Nat. Bur. Standards 80B (1976), 291-311.

SZ79

B. Sommer and J. G. Zabolitzky, On numerical Bessel transformation, Comput. Phys. Comm. 16 (1979), 383-387.

SZ81

I. A. Stegun and R. Zucker, Automatic computing methods for special functions. Part IV. Complex error function, Fresnel integrals, and other related functions, J. Res. Nat. Bur. Standards 86 (1981), 661-686.

Tal83

J. D. Talman, LSFBTR: A subroutine for calculating spherical Bessel transforms, Comput. Phys. Comm. 30 (1983), 93-99.

Tau92

G. Taubmann, Parabolic cylinder functions ${U}(n,x)$ for natural $n$ and positive $x$, Comput. Phys. Comm. 69 (1992), 415-419.

TB85

I. J. Thompson and A. R. Barnett, COULCC: A continued-fraction algorithm for Coulomb functions of complex order with complex arguments, Comput. Phys. Comm. 36 (1985), 363-372.

TB86

I. J. Thompson and A. R. Barnett, Coulomb and Bessel functions of complex arguments and order, J. Comput. Phys. 64 (1986), 490-509.

TB87

I. J. Thompson and A. R. Barnett, Modified Bessel functions ${I}_{\nu}(z)$ and ${K}_{\nu}(z)$ of real order and complex argument, to selected accuracy, Comput. Phys. Comm. 47 (1987), 245-257.

Tem75

N. M. Temme, On the numerical evaluation of the modified Bessel function of the third kind, J. Comput. Phys. 19 (1975), 324-337.

Tem76

N. M. Temme, On the numerical evaluation of the ordinary Bessel function of the second kind, J. Comput. Phys. 21 (1976), 343-350.

Tem77

N. M. Temme, The numerical computation of special functions by use of quadrature rules for saddle point integrals. I. Trapezoidal integration rules, Tech. Report TW 164/77, Mathematisch Centrum, Amsterdam, 1977.

Tem78

N. M. Temme, Some aspects of applied analysis: Asymptotics, special functions and their numerical computation, Mathematisch Centrum, Amsterdam, 1978.

Tem79

N. M. Temme, An algorithm with ALGOL 60 program for the computation of the zeros of ordinary Bessel functions and those of their derivatives, J. Comput. Phys. 32 (1979), 270-279.

Tem83

N. M. Temme, The numerical computation of the confluent hypergeometric function ${U}(a,b,z)$, Numer. Math. 41 (1983), 63-82.

Tem85

N. M. Temme, Special functions as approximants in uniform asymptotic expansions of integrals; a survey, Rend. Sem. Mat. Univ. Politec. Torino Fascicolo Speciale. Special Functions: Theory and Computation (1985), 289-317.

Tem87

N. M. Temme, On the computation of the incomplete gamma functions for large values of the parameters, Inst. Math. Appl. Conf. Ser. New Ser., vol. 10: Algorithms for Approximation (Shrivenham, 1985), Oxford Univ. Press, New York, 1987, pp. 479-489.

Tem92a

N. M. Temme, Asymptotic inversion of incomplete gamma functions, Math. Comp. 58 (1992), 755-764.

Tem92b

N. M. Temme, Asymptotic inversion of the incomplete beta function, J. Comput. Appl. Math. 41 (1992), 145-157.

Tem94a

N. M. Temme, Computational aspects of incomplete gamma functions with large complex parameters, Approximation and computation (West Lafayette, IN, 1993), Birkhäuser Boston, Boston, MA, 1994, pp. 551-562.

Tem94b

N. M. Temme, A set of algorithms for the incomplete gamma functions, Probab. Engrg. Inform. Sci. 8 (1994), 291-307.

Tem95

N. M. Temme, Asymptotics of zeros of incomplete gamma functions, Ann. Numer. Math. 2 (1995), 415-423.

Tho97

W. J. Thompson, Atlas for computing mathematical functions: an illustrated guide for practitioners, with programs in C and Mathematica, John Wiley & Sons Inc., New York, 1997, Includes CD-ROM. Fortran 90 edition exists also.

TM68

R. F. Tooper and J. Mark, Simplified calculation of $\operatorname{Ei}(x)$ for positive arguments, and a short table of $\operatorname{Shi}(x)$, Math. Comp. 22 (1968), 448-449.

TP83

N. Tubay and E. Panayirci, An efficient algorithm for generation of prolate spheroidal wave functions, Bull. Tech. Univ. Istanbul 36 (1983), 563-577.

TR69

T. Tamura and F. Rybicki, Coulomb functions for complex energies, Comput. Phys. Comm. 1 (1969), 25-30, for erratum see same journal v. 3 (1972), p. 276.

ULI90

Mathematical function library for Microsoft-C, United Laboratories, Inc., John Wiley & Sons, 1990, includes diskettes. Edition also exists in Fortran (1989).

Upo92

Ya. I. Upor, Calculation of zeros of orthogonal polynomials, Tbiliss. Gos. Univ. Inst. Prikl. Mat. Trudy 44 (1992), 110-127, 222.

vBBH70

A. L. van Buren, R. V. Baier, and S. Hanish, A Fortran computer program for calculating the oblate spheroidal radial functions of the first and second kind and their first derivatives, NRL Report No. 6959, Naval Res. Lab., Washington, D. C., 1970.

vBBHK72

A. L. van Buren, R. V. Baier, S. Hanish, and B. J. King, Calculation of spheroidal wave functions, J. Acoust. Soc. Amer. 51 (1972), 414-416.

vdLT84

C. G. van der Laan and N. M. Temme, Calculation of special functions: The gamma function, the exponential integrals and error-like functions, CWI Tract, vol. 10, Centrum voor Wiskunde en Informatica, Amsterdam, 1984.

VGK+91

V. K. Vlasov, M. N. Glukhova, L. N. Korolev, M. S. Pelina, S. N. Razumovski, and O. L. Ulasik, On the calculation of Bessel functions of a complex index and a complex argument, Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet. (1991), no. 3, 46-51, 64 (Russian).

VGK+92

V. K. Vlasov, M. N. Glukhova, L. N. Korolev, S. N. Razumovski, and O. L. Ulasik, On the calculation of the Mathieu functions, Vestnik Moskov. Univ. Ser. XV Vychisl. Mat. Kibernet. 1992 (1992), no. 1, 65-69.

VGRZ97

M. N. Vrahatis, T. N. Grapsa, O. Ragos, and F. A. Zafiropoulos, On the localization and computation of zeros of Bessel functions, Z. Angew. Math. Mech. 77 (1997), no. 6, 467-475.

VRS+95

M. N. Vrahatis, O. Ragos, T. Skiniotis, F. A. Zafiropoulos, and T. N. Grapsa, RFSFNS: A portable package for the numerical determination of the number and the calculation of roots of Bessel functions, Comput. Phys. Comm. 92 (1995), 252-266, for corrections see same journal v. 117 (1990), p. 290.

VRS+97

M. N. Vrahatis, O. Ragos, T. Skiniotis, F. A. Zafiropoulos, and T. N. Grapsa, The topological degree theory for the localization and computation of complex zeros of Bessel functions, Numer. Funct. Anal. Optim. 18 (1997), no. 1-2, 227-234.

VRZG96

M. N. Vrahatis, O. Ragos, F. A. Zafiropoulos, and T. N. Grapsa, Locating and computing zeros of Airy functions, Z. Angew. Math. Mech. 76 (1996), no. 7, 419-422.

vVNZ94

M. van Veldhuizen, R. Nieuwenhuizen, and W. Zijl, A note on log scale Hankel transforms, J. Computational Phys. 110 (1994), 196-199.

Wal84

J. L. Walmsley, On the efficient evaluation of modified Bessel functions of zeroth and first orders for arguments of the form $x\exp(i\pi/4)$, J. Comput. Phys. 56 (1984), 349-355.

War60

M. Ward, The calculation of the complete elliptic integral of the third kind, Amer. Math. Monthly 67 (1960), 205-213.

WBR82

C. A. Wills, J. M. Blair, and P. L. Ragde, Rational Chebyshev approximations for the Bessel functions ${J}_0(x), {J}_1(x), {Y}_0(x), {Y}_1(z)$, Math. Comp. 39 (1982), 617-623.

WC90

E. J. Weniger and J. Ciek, Rational approximations for the modified Bessel function of the second kind, Comput. Phys. Comm. 59 (1990), 471-493.

Wei94a

J. A. C. Weideman, Computation of the complex error function, SIAM J. Numer. Anal. 31 (1994), no. 5, 1497-1518, for correction see same journal v. 32 (1995), pp.330-331.

Wei94b

J. A. C. Weideman, Computing integrals of the complex error function, These proceedings, 1994.

WFQ92

Xi Liang Wang, Yong Cheng Feng, and Xian Ming Qing, Numerical computation of cylindrical functions for complex arguments, Dianzi Keji Daxue Xuebao 21 (1992), no. 2, 152-157.

Wie99

T. Wieder, Algorithm 794. Numerical Hankel transform by the Fortran program HANKEL, ACM Trans. Math. Software 25 (1999), 240-250.

Wim74

J. Wimp, On the computation of Tricomi's $\Psi$ function, Computing 13 (1974), 195-203.

Wim84

J. Wimp, Computation with recurrence relations, Pitman, London, 1984.

Wit68

B. F. W. Witte, Algorithm 332. Jacobi polynomials, Comm. ACM 11 (1968), 436-437, for remarks see same journal v. 13 (1970), p. 449 and v. 18 (1975), pp. 116-117.

WMC97

J. Wimp, P. McCabe, and J. N. L. Connor, Computation of Jacobi functions of the second kind for use in nearside-farside scattering theory, J. Comput. Appl. Math. 82 (1997), 447-464.

WNO94

T. Watanabe, M. Natoni, and T. Oguni (eds.), Mathematical software for the P.C. and workstations: A collection of Fortran 77 programs, Elsevier Science B.V., North-Holland, Amsterdam, 1994, includes diskette.

Wol99

S. Wolfram, The Mathematica book, fourth ed., Cambridge University Press, 1999, see also http://documents.wolfram.com/v4/.

Won89

R. Wong, Asymptotic approximations of integrals, Academic Press, New York, 1989.

Woo67

V. E. Wood, Chebyshev expansions for integrals of the error function, Math. Comp. 21 (1967), 494-496.

YKK88

A. Yu. Yeremin, I. E. Kaporin, and M. K. Kerimov, Computation of the derivatives of the Riemann zeta-function in the complex domain, U.S.S.R. Comput. Math. and Math. Phys. 28 (1988), no. 4, 115-124, see also [EKK85].

YM97

H. A. Yousif and R. Melka, Bessel function of the first kind with complex argument, Comput. Phys. Comm. 106 (1997), 199-206.

YN74

T. Yoshida and I. Ninomiya, Computation of Bessel functions ${K}_n(z)$ with complex argument by $\tau$-method, J. Inform. Process. 14 (1974), 32-37.

Yos92

T. Yoshida, Error analysis of the recurrence technique for calculation of Bessel functions ${I}_{\nu} (x)$, J. Inform. Process. 15 (1992), 213-221.

Yos95

Toshio Yoshida, Computation of Kummer functions ${U}(a,b,x)$ for large argument $x$ by using the $\tau$-method, Trans. Inform. Process. Soc. Japan 36 (1995), no. 10, 2335-2342.

Zan75

R. Zanovello, Sul calcolo numerico della funzione di Struve ${H}_{\nu}(z)$, Rend. Sem. Mat. Univ. Politec. Torino 32 (1975), 251-269.

ZB95

J. Zhang and J. A. Belward, Tau-method approximations for the Bessel function ${Y}_0(z)$, Comput. Math. Appl. 30 (1995), no. 7, 5-14.

ZB97

Jun Zhang and John A. Belward, Chebyshev series approximations for the Bessel function ${Y}\sb n(z)$ of complex argument, Appl. Math. Comput. 88 (1997), no. 2-3, 275-286.

ZGRV96

F. A. Zafiropoulos, T. N. Grapsa, O. Ragos, and M. N. Vrahatis, On the computation of zeros of Bessel and Bessel-related functions, Proceedings of the Sixth International Colloquium on Differential Equations (Plovdiv, 1995) (Utrecht), VSP, 1996, pp. 409-416.

Zha95

J. Zhang, Tau-method approximations for the Bessel function ${Y}_1(z)$, Comput. Math. Appl. 30 (1995), no. 7, 15-19.

Zha96a

J. Zhang, A note on the tau-method approximations for the Bessel functions ${Y}\sb 0(z)$ and ${Y}\sb 1(z)$, Comput. Math. Appl. 31 (1996), no. 9, 63-70.

Zha96b

J. Zhang, Symbolic and numerical computation on Bessel functions of complex argument and large magnitude, J. Comput. Appl. Math. 75 (1996), 99-118.

Ziv91

A. Ziv, Fast evaluation of elementary mathematical functions with correctly rounded last bit, ACM Trans. Math. Software 17 (1991), 410-423.

ZJ96

S. Zhang and J. Jin, Computation of special functions, John Wiley & Sons Inc., New York, 1996, Includes diskette with Fortran programs.

ZK95

Ya. M. Zhilekin and A. B. Kukarkin, A fast Fourier-Bessel transformation algorithm, Comput. Math. Math. Phys. 35 (1995), no. 7, 901-905.