SIAM AG on Orthogonal Polynomials and Special Functions


Extract from OP-SF NET

Compiled booklist

(This item first appeared in The Activity Group's Newsletter, February 1997, and in OP-SF NET 4.2, Topic #12. The following is based on the revised list published in the June 1997 Newsletter, with some revisions on January 28, 1998.)

From: Wolfram Koepf (
Subject: Compiled Booklist

Here I give the announced list of books and survey papers that should give a basis for understanding the current trends and needs in OP-SF. Let me say that the given list can be neither complete nor perfect. If somebody feels that an important item is missing, please let me know.

Readers who are interested in classical orthogonal polynomials should probably first look at [Chihara], [NU], [Rainville], [Szego], or [Tricomi]; readers looking for applications in mathematical physics might consider [NU].

[Artin] Artin, E.: "The Gamma Function." Holt, Rinehart and Winston, New
York, 1964. 

[Askey1] Askey, R. A. (Ed.): "Theory and Application of Special
Functions".  Proceedings of an advanced seminar sponsored by the
Mathematics Research Center, University of Wisconsin-Madison, March
21-April 2, 1975. Academic Press, New York, 1975. 

[Askey2] Askey, R. A. (Ed.): "Orthogonal Polynomials and Special
Functions." Regional Conference Series in Applied Mathematics 21, SIAM,
Philadelphia, 1975. 

[AKS] Askey, R. A., Koornwinder, T. H. and Schempp, W. (Eds.):  "Special
Functions: Group Theoretical Aspects and Applications." Mathematics and
Its Applications, Vol. 18. Reidel, Dordrecht-Boston-Lancaster, 1984.

[AW3] Askey, R. A. and Wilson, J.: Some basic hypergeometric orthogonal
polynomials that generalize Jacobi polynomials. Memoirs Amer. Math. Soc.
319, Providence, Rhode Island, 1985. 

[Bailey] Bailey, W. N.:  "Generalized Hypergeometric Series". Cambridge
University Press, England, 1935;  reprinted 1964 by Stechert-Hafner
Service Agency, New York-London. 

[Carlson] Carlson, B. C.: "Special Functions of Applied Mathematics."
Academic Press, New York, 1977.

[Chihara] Chihara, T. S.: "An Introduction to Orthogonal Polynomials." 
Gordon and Breach Publ., New York, 1978.

[Freud] Freud, G.: "Orthogonale Polynome". Birkhauser, Basel, 1969;
English translation, Pergamon Press, Oxford, 1971.

[GR] Gasper, G. and Rahman, M.: "Basic Hypergeometric Series." 
Encyclopedia of Mathematics and Its Applications, Vol. 34.  Cambridge
University Press, 1990.

[Geronimus1] Geronimus, Ya. L.:  "Polynomials Orthogonal on a Circle and
Interval." International Series of Monographs on Pure and Applied
Mathematics, Vol. 18.  Pergamon Press, Oxford-London-New York-Paris, 1961.

[Geronimus2] Geronimus, Ya. L.:  Appendix to the Russian translation of
Szego's book "Orthogonal Polynomials." Staatsverlag fur 
physikalisch-mathematische Literatur, Moskau, 1962. 

[GHMM] Gottloeber, S., Haubold, H. J., Muecket, J.-P. and Mueller, V.:
"Early Evolution of the Universe and Formation of Structure."
Akademie-Verlag, Berlin, 1990.

[Henrici1] Henrici, P.: "Applied and Computational Complex Analysis, Vol. 1:
Power Series, Integration, Conformal Mapping, Location of Zeros." 
John Wiley & Sons, New York, 1974.

[Henrici2] Henrici, P.: "Applied and Computational Complex Analysis, Vol.
2:  Special Functions, Integral Transforms, Asymptotics, Continued
Fractions." John Wiley & Sons, New York, 1977. 

[Henrici3] Henrici, P.: "Applied and Computational Complex Analysis, Vol.
3: Discrete Fourier Analysis - Cauchy Integrals - Construction of
Maps- Univalent Functions." John Wiley & Sons, New York, 1986. 

[Hai-Yakubovich] Hai, Nguyen Thanh and Yakubovich, S. B.: "The Double
Mellin-Barnes Type Integrals and Their Applications to Convolution
Theory", World Scientific.  Series Soviet and East European Mathematics. 
Vol.6. 1992. 295 pp.

[Hua] Hua, L.K.: "Harmonic Analysis of Functions of Several Complex
Variables in the Classical Domains." Translations of Mathematical
Monographs, Vol. 6, Amer. Math. Soc., Providence, Rhode Island, 1963.

[Lebedev] Lebedev, N. N.:  "Special Functions and their Applications."
Translated and edited by Richard A. Silverman.  Dover Publications, New
York, 1972.

[LL] Levin, A. and Lubinsky, D. S.: "Christoffel Functions and
Orthogonal Polynomials for Exponential Weights on [-1,1]."
Memoirs of the American Mathematical Society, No.535, Vol. 11, 1994.

[LW] Lorentzen, L. and Waadeland, H.: "Continued Fractions with
Applications." Studies in Computational Mathematics, Vol. 3.
North-Holland, Amsterdam, 1992. 

[Lubinsky] Lubinsky, D. S.: "Strong Asymptotics for Extremal Errors and
Polynomials Associated with Erdos Type Weights."Pitman Research Notes in
Mathematics, Vol. 202, Longman, Harlow, Essex, 1989.

[LS] Lubinsky, D. S. and Saff, E. B.: "Strong Asymptotics for Extremal
Polynomials Associated with Exponential Weights." Lecture Notes in
Mathematics, Vol. 1305, Springer, Berlin, 1988.

[Luke] Luke, Y.L.: "The Special Functions and their Approximations."
Vols. 1 and 2, Academic Press, New York 1969.

[MH] Mathai, A. M. and Haubold, H. J.: "Modern Problems in Nuclear 
and Neutrino Astrophysics." Akademie-Verlag, Berlin, 1988.

[Miller1] Miller, W., Jr.: "Lie Theory and Special Functions." Academic
Press, New York, 1968.

[Miller2] Miller, W., Jr.: "Symmetry and Separation of Variables." 
Encyclopedia of Mathematics and Its Applications, Vol. 4.
Addison-Wesley, Reading, Massachusetts, 1977. 

[Nevai1] Nevai, P. G.:  "Orthogonal Polynomials." Memoirs Amer. Math. 
Soc., Vol. 213, Providence, Rhode Island, 1979.

[Nevai2] Nevai, P. (Ed.): "Orthogonal Polynomials: Theory and Practice." 
Proceedings of the NATO Advanced Study Institute on Orthogonal Polynomials
and Their Applications, Colombus, Ohio, U.S.A., May 22-June 3, 1989,
Kluwer Academic Publ., Dordrecht-Boston-London, 1990.

[NU] Nikiforov, A. F. and Uvarov, V. B.:  "Special Functions of
Mathematical Physics".  Translated from the Russian by R. P. Boas,
Birkhauser, Basel, 1988. 

[NSU] Nikiforov, A. F., Suslov, S. K. and Uvarov, V. B.: "Classical
Orthogonal Polynomials of a Discrete Variable." Springer-Verlag,
Berlin-Heidelberg-New York, 1991.

[NS] Nikishin, E. M. and Sorokin, V. N.:  "Rational Approximations and
Orthogonality." Translations of Mathematical Monographs 92, Amer. Math.
Soc., Providence, Rhode Island, 1991. 

[Olver] Olver, F. W. J.: "Asymptotics and Special Functions." Academic
Press, New York, 1974. (reprinted A. K. Peters, Wellesley, 1997) 

[Perron] Perron, O.: "Die Lehre von den Kettenbruchen." Teubner, Leipzig,
1913; second edition, Chelsea, New York, 1950. 

[PWZ] Petkovvsek, M., Wilf, H. S. and Zeilberger, D.:  "A=B." A. K.
Peters, Wellesley, 1996. 

[Rainville] Rainville, E. D.: "Special Functions". The MacMillan Co., New
York, 1960. 

[Richards] Richards, D. St. P. (Ed.):  "Hypergeometric Functions on
Domains of Positivity, Jack Polynomials, and Applications." Proceedings of
an AMS special session, March 22-23, 1991 in Tampa, FL, USA. Contemporary
Mathematics 138, Amer. Math. Soc., Providence, Rhode Island, 1992. 

[Ronveaux] Ronveaux, A. (Ed.): "Heun's Differential Equations."  Oxford
University Press, New York, 1995. 

[Shohat] Shohat, J. A. and Tamarkin, J. D. : "The Problem of Moments."
Amer. Math. Soc., Providence, Rhode Island, 1963. 

[Szego] Szego, G.: "Orthogonal Polynomials." Amer. Math. Soc. Coll. 
Publ., Vol. 23, New York, 1939;  4th Edition, 1975. 

[ST] Stahl, H. and Totik, V.:  "General Orthogonal Polynomials."
Encyclopedia of Mathematics and Its Applications.  Cambridge University
Press, Cambridge, 1992.

[Talman] Talman, J.: "Special Functions: a Group Theoretic Approach." W.
A. Benjamin, New York, 1968. 

[Temme] Temme, N. M.: "Special Functions. An Introduction to the Classical
Functions of Mathematical Physics." John Wiley & Sons Inc., New York,

[Totik] Totik, V.: "Weighted Approximation with Varying Weight."  Springer
Lecture Notes in Mathematics, Vol. 1569, Springer, Berlin, 1994. 

[Tricomi] Tricomi, F. G.: "Vorlesungen uber Orthogonalreihen." Grundlehren
der Mathematischen Wissenschaften 76, Springer-Verlag,
Berlin-Gottingen-Heidelberg, 1955. 

[VanAssche] Van Assche, W.:  "Asymptotics for Orthogonal Polynomials."
Lecture Notes Math. 1265, Springer, Berlin-Heidelberg-New York, 1987. 

[Vilenkin1] Vilenkin, N. Ya.:  "Special Functions and the Theory of Group
Representations."  Translations of Mathematical Monographs 22, Amer. 
Math.  Soc., Providence, Rhode Island, 1968.

[Vilenkin2] Vilenkin, N. Ya., and Klimyk, A. U.:  "Representation of Lie
Groups and Special Functions, Vols. 1-3, and "Recent Advances", Kluwer
Academic Publ., Dordrecht-Boston-London, 1992-1995. 

[Wall] Wall, H. S.: "Analytic Theory of Continued Fractions."  Chelsea,
Bronx, NY, 1973. 

[Wong] Wong, R.: "Asymptotic Approximations of Integrals." Academic Press,
New York, 1989. 

[Yakubovich-Luchko] Yakubovich, S. B. and Luchko, Yu. F.: "The
Hypergeometric Approach to Integral Transforms and Convolutions". Kluwer
Academic Publishers. Mathematics and Applications. Vol.287. 1994. 234 pp. 

[Yakubovich] Yakubovich, S. B.: "Index Transforms", World Scientific.
1996. 258 pp. 

The following are handbooks and other reference manuals for orthogonal polynomials and special functions.

[AS] Abramowitz, M. and Stegun, I. A.: "Handbook of Mathematical
Functions." Dover Publ., New York, 1964.

[Erdelyi1] Erdelyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.: 
"Higher Transcendental Functions, Vols. 1-3."  McGraw-Hill, New York,

[Erdelyi2] Erdelyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G.: 
"Tables of Integral Transforms, Vols. 1-2."  McGraw-Hill, New York, 1954. 

[GR] Gradshteyn, I. S. and Ryzhik, I. M.: "Table of Integrals, Series,
and Products."  Printed and CD-ROM Version.  Academic Press, San Diego,
California, 1996. 

[Han] Hansen, E. R.: "A Table of Series and Products." Prentice-Hall,
Englewood Cliffs, NJ, 1975. 

Koekoek, R and Swarttouw, R.F. "The Askey scheme of hypergeometric
orthogonal polynomials and its q-analogues," Delft University of Technology,
Faculty of Technical Mathematics and Informatics, Report 94-05, 1994;
revised version of February 20, 1996 obtainable by anonymous ftp from:, directory siam/opsf_new/koekoek_swarttouw,
or via World Wide Web:
hypertext version:

[MOS] Magnus, W., Oberhettinger, F. and Soni, R. P.:  "Formulas and
Theorems for the Special Functions of Mathematical Physics".  Springer,
Berlin-Heidelberg-New York, 1966. 

[Mathai] Mathai, A. M.: "A Handbook of Generalized Special Functions for
Statistical and Physical Sciences." Clarendon Press, Oxford, 1993. 

[PBM] Prudnikov, A.P., Brychkov, Yu.A. and Marichev, O.I.:  "Integrals and
Series, Vols.1-3."  Gordon and Breach Publ., New York, 1989-1990. 

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