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On a new class of summation formulas involving the generalized hypergeometric 2F2 polynomial


Citation

Rathie, Arjun Kumar and Kilicman, Adem (2014) On a new class of summation formulas involving the generalized hypergeometric 2F2 polynomial. Advances in Difference Equations, 2014. art. no. 43. pp. 1-10. ISSN 1687-1839; ESSN: 1687-1847

Abstract

The aim of this research paper is to establish a quite general transformation involving the generalized hypergeometric function. Extensions of Kummer’s first transformation, Gauss and Kummer summation, and its contiguous results are then applied to obtain a new class of summation formulas involving the generalized hypergeometric 2F2 polynomial, which have not previously appeared in the literature. A few well-known results obtained earlier by Kim et al. (Int. J. Math. Math. Sci. 2010:309503, 2010; Integral Transforms Spec. Funct. 23(6):435-444, 2012) and Exton have been obtained as special cases of our main findings.


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Additional Metadata

Item Type: Article
Divisions: Institute for Mathematical Research
DOI Number: https://doi.org/10.1186/1687-1847-2014-43
Publisher: SpringerOpen
Keywords: Generalized hypergeometric series; Extension of Gauss and Kummer summation theorems; Polynomial
Depositing User: Nurul Ainie Mokhtar
Date Deposited: 21 Dec 2015 11:23
Last Modified: 21 Dec 2015 11:23
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1186/1687-1847-2014-43
URI: http://psasir.upm.edu.my/id/eprint/34720
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