Hypergeometric Functions with Integral Parameter Differences

For a generalized hypergeometric function pFq(z) with positive integral differences between certain numerator and denominator parameters, a formula expressing the pFq(z) as a finite sum of lower-order functions is proved. From this formula, Minton's two summation theorems for p = q + 1, z = 1 are deduced, one of these under less restrictive conditions than assumed by Minton. ©1971 The American Institute of Physics Original language English Journal Journal of Mathematical Physics Volume 12 Issue number 2 Pages (from-to) 270-271 ISSN 0022-2488 DOIs https://doi.org/10.1063/1.1665587 Publication status Published - 1971 Bibliographical note Copyright (1971) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.