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

Ahmed Ali Atash

Ahmed Ali Atash

and

Hussein Saleh Bellehaj

Hussein Saleh Bellehaj

| Jul 01, 2018

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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.

eISSN:: 2444-8656
Language:: English

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Journal Subjects:: Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics

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