<abstract xmlns="http://www.w3.org/1999/xhtml">In this paper, we establish two general transformation formulas for Exton’s quadruple hypergeometric functions <italic>K</italic>5 and <italic>K</italic>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.</abstract>

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.

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

Applied Mathematics and Nonlinear Sciences

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...

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

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.

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

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

KeywordsTransformation 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.

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