2010/11/20 by Michael Milgram, Milgram, Michael
Mathematics · #26E99 #30B10 #30B40 #33B99 #33C20 (primary) #33F10 #68W30 #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Iterative Methods for Nonlinear Equations #Mathematical Physics (math-ph) #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.1011.4546
openalex publication_date 2010/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
By systematically applying ten well-known and inequivalent two-part relations between hypergeometric sums 3F2(...|1) to the published database of all such sums, 62 new sums are obtained. The existing literature is summarized, and many purportedly novel results extracted from that literature are shown to be special cases of these new sums. The general problem of finding elements contiguous to Watson's, Dixon's and Whipple's theorems is reduced to a simple algorithm suitable for machine computation. Several errors in the literature are corrected or noted. The present paper both summarizes and extends a previous work on this subject.