SOME NEW GENERAL SUMMATION FORMULAS CONTIGUOUS TO THE KUMMER’S FIRST SUMMATION THEOREM | ||||
| Journal of Fractional Calculus and Applications | ||||
| Volume 15, Issue 2, July 2024, Page 1-10 PDF (234.41 K) | ||||
| Document Type: Regular research papers | ||||
| DOI: 10.21608/jfca.2024.263032.1059 | ||||
 View on SCiNiTO | ||||
| Authors | ||||
Aarif Hussain Bhat  1; Mohd Idris Qureshi2; javid majid3
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| 1Jamia Millia Islamia, New Delhi india | ||||
| 2Jamia Millia Islamia. New Delhi, India | ||||
| 3Jamia Millia Islamia, New Delhi India | ||||
| Abstract | ||||
| Due to the great success of hypergeometric functions of one variable, a number of hypergeometric functions of two or more variables have been introduced and explored. The aim of this paper is to provide the extensions and generalizations of Kummer’s first summation theorem for the higher-order hypergeometric series, where numeratorial and denominatorial parameters differ by positive integers, in the form of r+2Fr+1[a, b, {nr + ζr} ; 1 + a − b + m, {ζr} ; −1], with suitable convergence conditions. Where ζr is set of complex or real numbers, {nr} is set of positive integers and suitable restrictions on the value of m. 1. INTRODUCTION AND PRELIMINARIES The enormous popularity and broad usefulness of the hypergeometric function 2F1 and the generalized hypergeometric functions pFq (p, q ∈ N0) of one variable have inspired and stimulated a large number of researchers to introduce and investigate hypergeometric functions of two or more variables (see, e.g., [3, 16, 7, 21]). | ||||
| Keywords | ||||
| Gamma function; Pochhammer symbol; Generalized hypergeometric function; K¨ummer’s theorem; Hypergeometric summation theorems | ||||
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