# Article ID: MTJPAM-D-19-00004

## Title: GENERAL SUMMATION FORMULAS FOR THE KAMPÉ DE FÉRIET FUNCTION

Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-19-00004; Volume 1 / Issue 1 / Year 2019, Pages 107-128

Document Type: Research Paper

Author(s): Junesang Choi a , Arjun K. Rathie b

aDepartment of Mathematics, Dongguk University, Gyeongju 38066, Republic of Korea

bDepartment of Mathematics, Vedant College of Engineering & Technology, Rajasthan Technical University Village: TULSI, Post: Jakhmund, District: BUNDI-323021, Rajasthan State, India

Received: 21 September 2019, Accepted: 27 October 2019, Available online: 28 November 2019.

Corresponding Author: Junesang Choi (Email address: junesang@dongguk.ac.kr)

Full Text: PDF

Abstract

Very recently by employing two well-known Euler’s transformations for the hypergeometric function, Liu and Wang established numerous general transformation formulas for the Kampé de Fériet function and deduced many new summation formulas for the Kampé de Fériet function by using classical summation theorems for the series 2F1 due to Kummer, Gauss and Bailey. Here, we aim to establish 176 interesting summation formulas for the Kampé de Fériet function in the form of 16 general summation formulas based on the transformation formulas due to Liu and Wang. The results are derived with the help of generalizations of Kummer’s summation theorem, Gauss’ second summation theorem and Bailey’s summation theorem established earlier by Lavoie et al. The 176 formulas for the Kampé de Fériet function are pointed out to contain 16 known formulas, which are also recalled as corollaries.

Keywords: Gamma function, Pochhammer symbol, Gauss’s hypergeometric function 2F1, Generalized hypergeometric function pFq, Kampé de Fériet function, Generalization of Kummer’s summation theorem, Generalization of Gauss’ second summation theorem, Generalization of Bailey’s summation theorem

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