On a Resolution of Another Isolated Case of a Kummer’s Quadratic Transformation for 2F1-Reference-Cited by-同舟云学术

On a Resolution of Another Isolated Case of a Kummer’s Quadratic Transformation for 2F1

Published:2023-02-20 Issue:2 Volume:12 Page:221
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Atia Mohamed¹²^ORCID,Al-Mohaimeed Ahmed¹

Affiliation:

1. Department of Mathematics, College of Science, Qassim University, Buraidah 51452, Saudi Arabia

2. Laboratory LR17ES11, University of Gabes, Gabès 6072, Tunisia

Abstract

It is well-known that the Kummer quadratic transformation formula is valid provided that its parameters fulfill some specific conditions (see Gradshteyn, Ryzhik, Tables of Integrals, Series and Products, 9.130, 9.134.1). Very recently, one of us established a new identity when one of these conditions is not fulfilled. In this paper, we aim to discuss another isolated case which completely different from the first. Moreover, in the end, we mention two interesting consequences of these two new results.

Funder

Deanship of Scientific Research, Qassim University

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/12/2/221/pdf

Reference11 articles.

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2. Uber die hypergeometrische reihe;Kummer;J. Reine Angew. Math.,1836

3. Gradshteyn, I.S., and Ryzhik, I.M. (2000). Tables of Integrals, Series and Products, Academic Press. [6th ed.].

4. Andrews, G., Askey, R., and Roy, R. (1999). Special Functions, Encyclopedia of Mathematics and Its Applications, Cambridge University Press.

5. Abramowitz, M., and Stegun, I.A. (1965). Handbook of Mathematical Functions, Dover.

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