Software Needs in Special Functions

. 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..