Applications of the Generalized Kummer’s Summation Theorem to Transformation Formulas and Generating Functions-Reference-Cited by-同舟云学术

Applications of the Generalized Kummer’s Summation Theorem to Transformation Formulas and Generating Functions

Published:2018-07-01 Issue:2 Volume:3 Page:331-338
ISSN:2444-8656
Container-title:Applied Mathematics and Nonlinear Sciences
language:en
Short-container-title:

Author:

Atash Ahmed Ali¹,Bellehaj Hussein Saleh

Affiliation:

1. Department of Mathematics , Aden University , Aden , Yemen

Abstract

Abstract In this paper, we establish two general transformation formulas for Exton’s quadruple hypergeometric functions K 5 and K 12 by application of the generalized Kummer’s summation theorem. Further, a number of generating functions for Jacobi polynomials are also derived as an applications of our main results.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Engineering (miscellaneous),Modeling and Simulation,General Computer Science

Link

https://www.sciendo.com/pdf/10.21042/AMNS.2018.2.00026

Reference8 articles.

1. H. Exton, (1976), Multiple Hypergeometric Functions and Applications, John Wiley and Sons, Halsted Press, New York.

2. H. Exton, (1982), Hypergeometric functions of three variables, J. Indian Acad. Maths. 4, 113–119.

3. H. Exton, (1982), Reducible double hypergeometric functions and associated integrals, An Fac. Ci. Univ. Porto, 63, 137–143.

4. J. L. Lavoie, F. Grondin and A. K. Rathie, (1996), Generalizations of Whipple’s theorem on the sum of a 3F2 Journal of Computational and Applied Mathematics, 72, 293–300. 10.1016/0377-0427(95)00279-0.

5. E. D. Rainville, (1960), Special Functions, The Macmillan Company, New York.

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