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Numerical Evaluation of Special Functions

D. W. Lozier and F. W. J. Olver

4.6. Polylogarithms .

4.6.1. Dilogarithms.


[ Luk75] .

Software Packages:

[ GZ75, Fortran] .

Intermediate Libraries:

[ Bak92] , [ Mos89] .

Comprehensive Libraries:


Interactive Systems:


4.6.2. Higher Polylogarithms.

Intermediate Libraries:

[ Bak92] .

Interactive Systems:


4.6.3. Articles.

[ GT81] , [ JL72] , [ Mor79] .


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

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

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.

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

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

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

S. L. B. Moshier, Methods and programs for mathematical functions, Ellis Horwood Limited, Chichester, 1989, separate diskette.


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:

Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742

E-mail address:

The research of the second author has been supported by NSF Grant CCR 89-14933.

1991 Mathematics Subject Classification. Primary 65D20; Secondary 33-00.

Daniel W Lozier
Fri Apr 7 13:56:11 EDT 1995