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Numerical Evaluation of Special Functions
D. W. Lozier and F. W. J. Olver
4.7. Zeta Function
4.7.1. Real Arguments.
[ Mar65, Algol]
4.7.2. Complex Arguments.
[ BD80, Fortran]
[ YKK88, Fortran]
[ Ker80, includes survey]
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.
L. Baker, C mathematical function handbook, McGraw-Hill, Inc., New
York, 1992, includes diskette.
A. Bañuelos and R. A. Depine, A program for computing the Riemann
zeta function for complex argument, Comput. Phys. Comm. 20 (1980),
W. J. Cody, K. E. Hillstrom, and H. C. Thacher, Jr., Chebyshev
approximations for the Riemann zeta function, Math. Comp. 25 (1971),
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].
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.
Y. L. Luke, The special functions and their approximations, vol. 2,
Academic Press, New York, 1969.
B. Markman, Contribution no. 14. The Riemann zeta function, BIT
5 (1965), 138--141.
S. L. B. Moshier, Methods and programs for mathematical functions, Ellis
Horwood Limited, Chichester, 1989, separate diskette.
R. Piessens and M. Branders, Chebyshev polynomial expansions of the
Riemann zeta function, Math. Comp. 26 (1972), 1022.
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
This document is an excerpt from the current hypertext version of
an article that appeared in Walter Gautschi (ed.),
Mathematics of Computation 1943--1993: A Half-Century of
Computational Mathematics, Proceedings of Symposia in
Applied Mathematics 48, American Mathematical Society,
Providence, RI 02940, 1994.
The symposium was held at the University of British Columbia
August 9--13, 1993, in honor of the fiftieth anniversary of
the journal Mathematics of Computation.
The original abstract follows.
Higher transcendental functions continue to play varied and
important roles in investigations by engineers, mathematicians,
scientists and statisticians.
The purpose of this paper is to assist in locating useful approximations
and software for the numerical generation of these functions, and to
offer some suggestions for future developments in this field.
Applied and Computational Mathematics Division,
National Institute of Standards and Technology,
Gaithersburg, Md 20899
E-mail address: firstname.lastname@example.org
Institute for Physical Science and Technology,
University of Maryland,
College Park, MD 20742
E-mail address: email@example.com
The research of the second author has been supported by NSF
Grant CCR 89-14933.
1991 Mathematics Subject Classification. Primary 65D20;
Daniel W Lozier
Fri Apr 7 13:57:20 EDT 1995