Article
Applications of the Generalized Kummer’s Summation Theorem to Transformation Formulas and Generating Functions
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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.
Keywords
Transformation formulas, Generating functions, generalized Kummer’s theorem, Exton functions, Saran functions, Jacobi polynomials, 33B15, 33C05, 33C45
Citation
Atash, A. A. & Bellehaj, H. S. (2018). Applications of the generalized kummer’s summation theorem to transformation formulas and generating functions. Applied Mathematics and Nonlinear Sciences, 3(2), 331–338. https://doi.org/10.21042/AMNS.2018.2.00026
A. A. Atash and H. S. Bellehaj, “Applications of the generalized kummer’s summation theorem to transformation formulas and generating functions,” Applied Mathematics and Nonlinear Sciences, vol. 3, no. 2, pp. 331–338, 2018, doi: 10.21042/AMNS.2018.2.00026.
Atash AA, Bellehaj HS. Applications of the generalized kummer’s summation theorem to transformation formulas and generating functions. Applied Mathematics and Nonlinear Sciences. 2018;3(2):331–338. doi:10.21042/AMNS.2018.2.00026.
Atash, A. A. and Bellehaj, H. S. (2018), ‘Applications of the generalized kummer’s summation theorem to transformation formulas and generating functions’, Applied Mathematics and Nonlinear Sciences, 3(2), pp. 331–338. Available at: https://doi.org/10.21042/AMNS.2018.2.00026.
Atash, Ahmed Ali, and Hussein Saleh Bellehaj. “Applications of the Generalized Kummer’s Summation Theorem to Transformation Formulas and Generating Functions.” Applied Mathematics and Nonlinear Sciences, vol. 3, no. 2, 2018, pp. 331–338. https://doi.org/10.21042/AMNS.2018.2.00026.
Atash, Ahmed Ali, and Hussein Saleh Bellehaj. “Applications of the Generalized Kummer’s Summation Theorem to Transformation Formulas and Generating Functions.” Applied Mathematics and Nonlinear Sciences 3, no. 2 (2018): 331–338. https://doi.org/10.21042/AMNS.2018.2.00026.
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Published by: Engineering Journals
