Automatic computing methods for special functions

Abstract

AMS55[1)1 the Handbook of Mathematical Func tion s -in add ition to definin g fu nctions in te rms of their integrals, power series, asymptotic expansion s, e tc., also suppli es tables a nd approximating polynomial s as welJ as methods of co mputing values both within and outside th e tabular range. With the present trend to large scale co mputer sys tems, questions frequently arise concerning methods of co mputing the tabular values th emselves. In many, if not most cases, the method used for computing th e table is certainly not the bes t method for computing discrete values. While many specialized me thods and programs exis t [3,6,7,8 1, as a supple ment to the Handbook and to satisfy general need s, a sys l.ematic effort is being made to supply methods of computing special func60ns, accurate within machine precision, valid throughout the entire range of th e fun ction , efficient , and readily programmable and adaptable for varying precision and computers. Part I of the present paper is devoted to the error , probability, and related fun ctions.