- Next: 1. Introduction

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

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.
*

** 3. Packages, Libraries and Systems
**

** 5. Functions of Two or More Variables
**

** 6. Testing and Library Construction
**

We are grateful to the following individuals for supplying references and making helpful comments: D. E. Amos, W. L. Anderson, A. R. Barnett, E. Battiste, C. Brezinski, B. C. Carlson, B. Gabutti, P. W. Gaffney, W. Gautschi, K. S. Kölbig, S. D. Leigh, L. C. Maximon, M. A. McClain, B. R. Miller, W. Parke, N. M. Temme, M. Vuorinen.

In the references that follow, the acronyms within the identifying
square brackets follow the AMS BibTeX scheme.
Initial letters pertain to the author(s) or editor(s).
These are followed by two digits representing the year of publication;
a letter may also be appended to distinguish between publications
in the same year, e.g. [** AB87a**]
, [** AB87b**]
.
In the case of papers or books with more than four authors,
initial letters from the names of the first three authors are used,
followed by a sign, e.g. [** ADK+84**]
.
** It is also important to note that the references are listed
according to the alphabetical order of the acronyms and not according to
the alphabetical order of the authors' names**.

**AB87a**-
G. Allasia and R. Besenghi,
*Numerical calculation of incomplete gamma functions by the trapezoidal rule*, Numer. Math.**50**(1987), 419--428. **AB87b**-
G. Allasia and R. Besenghi,
*Numerical computation of Tricomi's psi function by the trapezoidal rule*, Computing**39**(1987), 271--279. **ADK84**-
A. A. Abramov, A. L. Dyshko, N. B. Konyukhova, T. V. Pak, and B. S. Pariiskii,
*Evaluation of prolate spheroidal function by solving the corresponding differential equations*, U.S.S.R. Comput. Math. and Math. Phys.**24**(1984), no. 1, 1--11.

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 13:28:57 EDT 1995