- Grandparent: 0. Numerical Evaluation of Special Functions
- Parent: 4. Functions of One Variable
- Previous: 4.5. Landau Density and Distribution Functions
- Next: 4.7. Zeta Function

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

** 4.6. Polylogarithms
. **

4.6.1. * Dilogarithms. *

Algorithms:

[** Luk75**]
.

Software Packages:

[** GZ75**, Fortran]
.

Intermediate Libraries:

[** Bak92**]
,
[** Mos89**]
.

Comprehensive Libraries:

** IMSL**,
** SLATEC**.

Interactive Systems:

** Maple**.

4.6.2. * Higher Polylogarithms. *

Intermediate Libraries:

[** Bak92**]
.

Interactive Systems:

** Mathematica**.

4.6.3. * Articles. *

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

**Bak92**-
L. Baker,
*C mathematical function handbook*, McGraw-Hill, Inc., New York, 1992, includes diskette. **GT81**-
R. Gastmans and W. Troost,
*On the evaluation of polylogarithmic integrals*, Simon Stevin**55**(1981), 205--219. **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. **JL72**-
D. Jacobs and F. Lambert,
*On the numerical calculation of polylogarithms*, BIT**12**(1972), 581--585. **Luk75**-
Y. L. Luke,
*Mathematical functions and their approximations*, Academic Press, New York, 1975. **Mor79**-
R. Morris,
*The dilogarithm function of a real argument*, Math. Comp.**33**(1979), 778--787. **Mos89**-
S. L. B. Moshier,
*Methods and programs for mathematical functions*, Ellis Horwood Limited, Chichester, 1989, separate diskette.

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: dlozier@nist.gov*

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

* E-mail address: olver@bessel.umd.edu*

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

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

Fri Apr 7 13:56:11 EDT 1995