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# Numerical Evaluation of Special Functions

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

** 3. Packages, Libraries and Systems
**

This section reviews a selection of mathematical software with
respect to its support for the numerical evaluation of special
functions.
In some cases only a descriptive overview is given while in
others cross references by individual function are given in
the subsequent sections § 4 and § 5.
The cross-referenced packages, libraries and systems are marked with
a .
We used the following criteria in assigning the marks:

First, a marked item must be readily accessible.
Often this means it is commercial software that is purchased or
leased for a fee
but we also include software that is distributed, sometimes over
computer networks, by journals and research institutions.

Second, a marked item must have a
significant following in North America.
(In most cases the unmarked software is used widely elsewhere.)

Third, a marked item must be reasonably comprehensive in its
coverage of special functions.

** 3.1. Software Packages
. **

** 3.2. Intermediate Libraries
. **

** 3.3. Comprehensive Libraries
. **

** 3.4. Interactive Systems
. **

**Dev93**-
K. Devlin (ed.),
* Computers and mathematics*, Notices Amer. Math. Soc.
** 40** (1993), 613--623.

### Abstract:

*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: 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.

- ...functions
- General reviews of mathematical software appear
regularly in the Computers and Mathematics column of the
* Notices
of the American Mathematical Society*. A useful guide to these
reviews is given in [** Dev93**]
.

*Daniel W Lozier *

Fri Apr 7 13:34:11 EDT 1995