STUDY ON $k$-GAUSS SECOND SUMMATION THEOREMS AND $k$-KUMMER'S TRANSFORMATION

Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 149

Volume : 16 , Issue : 3
DOI:
Author :
Ekta Mittal (Department of Mathematics, IIS Deemed to be University, Jaipur - 302020, INDIA)
Sunil Joshi (Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur - 303007, INDIA)

Abstract

The aim of the present investigation is to create some summation theorems like Gauss, Bailey, and Kummer in the form of $k$- hypergeometric function. Further, we develop a new class of Kummer’s differential equation of $k$-parameter and Kummer’s transformations formulae in terms $k$- confluent hypergeometric function.

Keywords and Phrases

$k$-Gamma function, $k$-Beta function, $k$-hypergeometric functions, $k$-pochhammer symbols.

A.M.S. subject classification

33E12, 44A10, 33B15.

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