Polynomial series expansions for confluent and Gaussian hypergeometric functions

Abstract

Based on the Hadamard product of power series, polynomial series expansions for confluent hypergeometric functions M(a, c;.) and for Gaussian hypergeometric functions F(a,b;c;.) are introduced and studied It turns out that the partial sums provide an interesting alternative for the numerical evaluation of the functions M(a,c;.) and F(a.b;c:.), in particular, if the parameters are also viewed as variables.