On Hypergeometric 3F2(1)

Abstract

By systematically applying ten inequivalent two-part relations between hypergeometric sums 3F2(1) to the published database of all such sums, 66 new sums are obtained. Many results extracted from the literature are shown to be special cases of these new sums. In particular, the general problem of finding elements contiguous to Watson's, Dixon's and Whipple's theorem is reduced to a simple algorithm suitable for machine computation. Several errors in the literature are corrected or noted.