On a new class of summation formulas involving the generalized hypergeometric 2F2 polynomial
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2014
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| Online Access: | http://psasir.upm.edu.my/id/eprint/34720/1/On%20a%20new%20class%20of%20summation%20formulas.pdf |
| _version_ | 1825948504891064320 |
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| author | Rathie, Arjun Kumar Kilicman, Adem |
| author_facet | Rathie, Arjun Kumar Kilicman, Adem |
| author_sort | Rathie, Arjun Kumar |
| collection | UPM |
| description | 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. |
| first_indexed | 2024-03-06T08:29:51Z |
| format | Article |
| id | upm.eprints-34720 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T08:29:51Z |
| publishDate | 2014 |
| publisher | SpringerOpen |
| record_format | dspace |
| spelling | upm.eprints-347202015-12-21T11:23:22Z http://psasir.upm.edu.my/id/eprint/34720/ On a new class of summation formulas involving the generalized hypergeometric 2F2 polynomial Rathie, Arjun Kumar Kilicman, Adem 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. SpringerOpen 2014-01 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/34720/1/On%20a%20new%20class%20of%20summation%20formulas.pdf 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 http://www.advancesindifferenceequations.com/content/2014/1/43/abstract 10.1186/1687-1847-2014-43 |
| spellingShingle | Rathie, Arjun Kumar Kilicman, Adem On a new class of summation formulas involving the generalized hypergeometric 2F2 polynomial |
| title | On a new class of summation formulas involving the generalized hypergeometric 2F2 polynomial |
| title_full | On a new class of summation formulas involving the generalized hypergeometric 2F2 polynomial |
| title_fullStr | On a new class of summation formulas involving the generalized hypergeometric 2F2 polynomial |
| title_full_unstemmed | On a new class of summation formulas involving the generalized hypergeometric 2F2 polynomial |
| title_short | On a new class of summation formulas involving the generalized hypergeometric 2F2 polynomial |
| title_sort | on a new class of summation formulas involving the generalized hypergeometric 2f2 polynomial |
| url | http://psasir.upm.edu.my/id/eprint/34720/1/On%20a%20new%20class%20of%20summation%20formulas.pdf |
| work_keys_str_mv | AT rathiearjunkumar onanewclassofsummationformulasinvolvingthegeneralizedhypergeometric2f2polynomial AT kilicmanadem onanewclassofsummationformulasinvolvingthegeneralizedhypergeometric2f2polynomial |