The Sums of a Double Hypergeometric Series and of the First m+1 Terms of 3F2(a,b,c;(a+b+1)/2,2c;1) when c = -m is a Negative Integer

2014/12/12 by Charles F. Dunkl, Dunkl, Charles F., George Gasper +1
Computer Science · Mathematics · #33C20 #33C70 #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Polynomial and algebraic computation #math.CA #msc:33C20 #msc:33C70

paper · pdf · doi:10.48550/arxiv.1412.4022

7 pages, added general remarks, another derivation of one of the formulas, and references to related results in basic hypergeometric series

openalex publication_date 2014/12/12 · arxiv created 2014/12/16 · arxiv updated 2014/12/17 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

A summation formula is derived for the sum of the first m+1 terms of the 3F2(a,b,c;(a+b+1)/2,2c;1) series when c = -m is a negative integer. This summation formula is used to derive a formula for the sum of a terminating double hypergeometric series that arose in another project by one of us (C.D.)

Related

• A summation formula for a ₃F₂(1) hypergeometric series
• An Entry of Ramanujan on Hypergeometric Series in his Notebooks
• An alternative proof of the extended Saalschutz summation theorem for the r+3Fr+2(1) series with applications
• On Hypergeometrics 3F2(1) - A Review
• On Hypergeometric 3F2(1)