Evaluations of some terminating hypergeometric ₂F₁(2) series

2014/03/30 by Y S Kim, Kim, Y S, Arjun K. Rathie +5
Mathematics · #33C15 #33C20 #Advanced Mathematical Identities #Complex Variables (math.CV) #FOS: Mathematics #Iterative Methods for Nonlinear Equations #Mathematical functions and polynomials #math.CV #msc:33C15 #msc:33C20

paper · pdf · doi:10.48550/arxiv.1403.7759

7 pages, no figures

arxiv created 2014/03/30 · openalex publication_date 2014/03/30 · arxiv updated 2014/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Explicit expressions for the hypergeometric series ₂F₁(-n, a; 2a± j;2) and ₂F₁(-n, a; -2n± j;2) for positive integer n and arbitrary integer j are obtained with the help of generalizations of Kummer's second and third summation theorems obtained earlier by Rakha and Rathie. Results for |j|≤ 5 derived previously using different methods are also obtained as special cases.

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