2017/10/22 by Sergei Kalmykov, Kalmykov, S. I., Dmitrii Karp +1 · 1 citation
Mathematics · #33C15 #33C20 #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematical functions and polynomials
paper · pdf · doi:10.48550/arxiv.1710.07889
openalex publication_date 2017/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently, Feng, Kuznetsov and Yang discovered a very general reduction formula for a sum of products of the generalized hypergeometric functions (J. Math. Anal. Appl. 443(2016), 116--122). The main goal of this note is to present a generalization of a particular case of their identity when the generalized hypergeometric function is reduced to the Kummer function 1F1. Our generalized formula contains an additional integer shift in the bottom parameter of the Kummer function. The key ingredient of the proof is a summation formula for the Clausen series 3F2(1) with two integral parameter differences of opposite sign. In the ultimate section of the paper we prove another formula for a particular product difference of the Kummer functions in terms of a linear combination of these functions.