. 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. 5.9. Mathieu, Lam'e, and Spheroidal Wave Functions. 5.9.1. Characteristic Values of Mathieu's Equation. Software Packages:...

. Currently available software for special functions exhibits gaps and defects in comparison to the needs of modern high-performance scientific computing and also, surprisingly, in comparison to what could be constructed from current algorithms. In this paper we expose some of these deficiencies and identify the related need for user-oriented testing software. 1. Introduction A recent article by Lozier and Olver [21] provides a survey of algorithms and software for the numerical evaluation of special functions. Its emphasis is on the generation of function values although selected resources for zeros and integrals are included also. Journals, books, conference proceedings, and software documents were examined and a bibliography of nearly 500 references was constructed. Based on this investigation, the functions were classified and cross-referenced to bibliographic entries and to specific software libraries and systems 1 . The bibliography was prepared using the authors' professional...

This is a proposal to develop a software test service at the National Institute of Standards and Technology for use in testing the accuracy, or numerical precision, of mathematical software for special functions. The service would use the World Wide Web to receive test requests and return test results. The tests would be run on a network of workstations at the Institute. It is hoped that such a service will be of practical utility to anyone who uses special functions in physics or other applications, and that it will stimulate the interest of applied mathematicians who are interested in the computation of special functions as well as computer scientists who are interested in innovative uses of the Internet. The author solicits comments on any aspect of the proposed service. 1 Introduction Mathematical software is deeply embedded in the computing environment. Since this environment is evolving rapidly, its impact on mathematical software needs to be revisited regularly. Progress in p...

. 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. 4.7. Zeta Function. 4.7.1. Real Arguments. Algorithms: [CHT71], [Luk69b], [PB72]. Software Packages: [Mar65, Algol]. Intermediate Libr...