Acta mathematica scientia,Series A ›› 2025, Vol. 45 ›› Issue (1): 136-152.

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Reduction and Summation Formulas for Two Types of Kampé de Fériet Series

Liu Hongmei, Li Yang   

  1. School of Science, Dalian Minzu University, Liaoning Dalian 116600
  • Received:2023-08-30 Revised:2024-08-15 Online:2025-02-26 Published:2025-01-08

Abstract: Two $ _3F_2[1] $-summation theorems are employed to establish two general transformation formulas for double infinite series. With the help of some classical hypergeometric series summation formulas, the two transformations yield a number of summation formulas for Kampé de Fériet series of type $ F_{q:1;0}^{p:2;1} $. Furthermore a list of reduction and transformation formulas for Kampé de Fériet series of type $ F_{q:1;1}^{p:2;2} $ are derived by utilizing four Saalschützian $ _4F_3[1] $-summation formulas.

Key words: hypergeometric series, Kampé de Fériet series, reduction and summation formulas

CLC Number: 

  • O174.6
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