NDLI: Reduction Formulas for Generalized Hypergeometric Series Associated with New Sequences and Applications

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Reduction Formulas for Generalized Hypergeometric Series Associated with New Sequences and Applications

Content Provider	MDPI
Author	Choi, Junesang Qureshi, Mohd Idris Bhat, Aarif Hussain Majid, Javid
Copyright Year	2021
Abstract	In this paper, by introducing two sequences of new numbers and their derivatives, which are closely related to the Stirling numbers of the first kind, and choosing to employ six known generalized Kummer’s summation formulas for $_{2} F_{1} (- 1)$ and $_{2} F_{1} (1 / 2)$ , we establish six classes of generalized summation formulas for $_{p + 2} F_{p + 1}$ with arguments $- 1$ and $1 / 2$ for any positive integer p. Next, by differentiating both sides of six chosen formulas presented here with respect to a specific parameter, among numerous ones, we demonstrate six identities in connection with finite sums of $_{4} F_{3} (- 1)$ and $_{4} F_{3} (1 / 2)$ . Further, we choose to give simple particular identities of some formulas presented here. We conclude this paper by highlighting a potential use of the newly presented numbers and posing some problems.
Starting Page	150
e-ISSN	25043110
DOI	10.3390/fractalfract5040150
Journal	Fractal and Fractional
Issue Number	4
Volume Number	5
Language	English
Publisher	MDPI
Publisher Date	2021-10-01
Access Restriction	Open
Subject Keyword	Fractal and Fractional Logic Gamma Function Psi Function Pochhammer Symbol Hypergeometric Function 2f1 Generalized Hypergeometric Functions Tfu Gauss's Summation Theorem for 2f1(1) Kummer's Summation Theorem for 2f1(−1) Generalized Kummer's Summation Theorem for 2f1(−1) Stirling Numbers of the First Kind
Content Type	Text
Resource Type	Article

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