2015/06/25 by Mark W. Coffey, Coffey, Mark W.
Mathematics · #05A10 #33C20 #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical functions and polynomials #math.CA #math.CO #msc:05A10 #msc:33C20
paper · pdf · doi:10.48550/arxiv.1506.09160
13 pages, no figures
arxiv created 2015/06/25 · openalex publication_date 2015/06/25 · arxiv updated 2015/07/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We principally present reductions of certain generalized hypergeometric functions 3F2(± 1) in terms of products of elementary functions. Most of these results have been known for some time, but one of the methods, wherein we simultaneously solve for three alternating binomial sums, may be new. We obtain a functional equation holding for all three of this set of alternating binomial sums. Using successive derivatives, we show how related chains of 3F2(± 1) values may be obtained. It may be emphasized that we make no reliance on the WZ method for hypergeometric summation. Additional material on Pochhammer symbols and certain of their products is presented in an Appendix to supplement the pedagogical content of the paper.