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

Ahmed Ali Atash

Atash, Ahmed Ali

and

Hussein Saleh Bellehaj

Bellehaj, Hussein Saleh

Jul 01, 2018

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

Applied Mathematics and Nonlinear Sciences

Volume 3 (2018): Issue 2 (July 2018)

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Published Online: Jul 01, 2018

Page range: 331 - 338

Received: Jan 04, 2018

Accepted: Jul 01, 2018

DOI: https://doi.org/10.21042/AMNS.2018.2.00026

Keywords
Transformation formulas, Generating functions, generalized Kummer’s theorem, Exton functions, Saran functions, Jacobi polynomials

© 2018 Ahmed Ali Atash and Hussein Saleh Bellehaj, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In this paper, we establish two general transformation formulas for Exton’s quadruple hypergeometric functions K₅ and K₁₂ 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.

Language:: English

Publication timeframe:: 1 times per year
Journal Subjects:: Life Sciences, Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics, Physics, other

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