English

On Hypergeometrics 3F2(1) - A Review

Classical Analysis and ODEs 2010-11-23 v1 Mathematical Physics math.MP

Abstract

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.

Keywords

Cite

@article{arxiv.1011.4546,
  title  = {On Hypergeometrics 3F2(1) - A Review},
  author = {Michael Milgram},
  journal= {arXiv preprint arXiv:1011.4546},
  year   = {2010}
}

Comments

34 pages. This is an extension of a previous paper: arxiv.org/abs/math/0603096

R2 v1 2026-06-21T16:46:28.492Z