Some multivariable Gaussian hypergeometric extensions of the Preece theorem
Some generalisations of the Preece theorem involving the product of two Kummer's functions 1F1 are obtained using Dixon's theorem and some well-known identities. Its special cases yield various new transformations and reduction formulae involving Pathan's quadruple hypergeometric func...
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| Vydané v: | The ANZIAM journal Ročník 48; číslo 1; s. 143 - 150 |
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| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Cambridge, UK
Cambridge University Press
01.07.2006
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| ISSN: | 1446-1811, 1446-8735 |
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| Abstract | Some generalisations of the Preece theorem involving the product of two Kummer's functions 1F1 are obtained using Dixon's theorem and some well-known identities. Its special cases yield various new transformations and reduction formulae involving Pathan's quadruple hypergeometric function and Srivastava's quadruple hypergeometric function F(4) and triple hypergeometric function F(3). Some known results of Preece, Pathan and Bailey are also obtained as special cases. |
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| AbstractList | Some generalisations of the Preece theorem involving the product of two Kummer's functions
1
F
1
are obtained using Dixon's theorem and some well-known identities. Its special cases yield various new transformations and reduction formulae involving Pathan's quadruple hypergeometric function
and Srivastava's quadruple hypergeometric function
F
(4)
and triple hypergeometric function
F
(3)
. Some known results of Preece, Pathan and Bailey are also obtained as special cases. Some generalisations of the Preece theorem involving the product of two Kummer's functions 1F1 are obtained using Dixon's theorem and some well-known identities. Its special cases yield various new transformations and reduction formulae involving Pathan's quadruple hypergeometric function and Srivastava's quadruple hypergeometric function F(4) and triple hypergeometric function F(3). Some known results of Preece, Pathan and Bailey are also obtained as special cases. |
| Author | Sadiq Khan, M. Khan, N. U. Pathan, M. A. Qureshi, M. I. |
| Author_xml | – sequence: 1 givenname: M. I. surname: Qureshi fullname: Qureshi, M. I. organization: 1Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia, New Delhi-110025, India – sequence: 2 givenname: M. surname: Sadiq Khan fullname: Sadiq Khan, M. email: mohdsadiq786@rediffmail.com. organization: 2Department of Mathematics, Shibli National College, Paharpur, Azamgarh, U.P., India; e-mail: mohdsadiq786@rediffmail.com – sequence: 3 givenname: M. A. surname: Pathan fullname: Pathan, M. A. email: mapathan@gmail.com organization: 3Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India; e-mail: mapathan@gmail.com, nabi-khan@rediffmail.com – sequence: 4 givenname: N. U. surname: Khan fullname: Khan, N. U. email: mapathan@gmail.com organization: 3Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India; e-mail: mapathan@gmail.com, nabi-khan@rediffmail.com |
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| Cites_doi | 10.1007/BF03012437 10.1093/qmath/4.1.237 10.1016/S1385-7258(79)80012-8 10.1112/plms/s2-22.1.370 |
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| References | Exton (S1446181100003473_ref003) 1982; 4 Srivastava (S1446181100003473_ref009) 1971; 26 Pathan (S1446181100003473_ref005) 1978; 9 Srivastava (S1446181100003473_ref010) 1976; 63 S1446181100003473_ref006 S1446181100003473_ref007 S1446181100003473_ref004 S1446181100003473_ref001 Srivastava (S1446181100003473_ref013) 1984 Exton (S1446181100003473_ref002) 1976 Srivastava (S1446181100003473_ref011) 1969; 31 Rainville (S1446181100003473_ref008) 1960 Srivastava (S1446181100003473_ref012) 1985 |
| References_xml | – volume: 31 start-page: 449 year: 1969 ident: S1446181100003473_ref011 article-title: Certain generalized Neumann expansions associated with Kampé de Fériet function publication-title: Nederl. Akad. Wetensch. Proc. Ser. A – volume: 9 start-page: 1113 year: 1978 ident: S1446181100003473_ref005 article-title: On some transformations of triple hypergeometric series F(3)-III publication-title: Indian J. Pure Appl. Math. – ident: S1446181100003473_ref004 doi: 10.1007/BF03012437 – volume: 26 start-page: 35 year: 1971 ident: S1446181100003473_ref009 article-title: A formal extension of certain generating functions-II publication-title: Glasnik Mat. Ser. III – ident: S1446181100003473_ref001 doi: 10.1093/qmath/4.1.237 – volume-title: Multiple hypergeometric functions and applications year: 1976 ident: S1446181100003473_ref002 – ident: S1446181100003473_ref006 doi: 10.1016/S1385-7258(79)80012-8 – volume-title: Special functions year: 1960 ident: S1446181100003473_ref008 – volume-title: A Treatise on Generating Functions year: 1984 ident: S1446181100003473_ref013 – volume: 4 start-page: 113 year: 1982 ident: S1446181100003473_ref003 article-title: Hypergeometric functions of three variables publication-title: J. Indian Acad. Math. – ident: S1446181100003473_ref007 doi: 10.1112/plms/s2-22.1.370 – volume: 63 start-page: 445 year: 1976 ident: S1446181100003473_ref010 article-title: Generalized Neumann expansions involving hypergeometric functions publication-title: Proc. Cambridge Philos. Soc. – volume-title: Multiple Gaussian Hypergeometric Series year: 1985 ident: S1446181100003473_ref012 |
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| Snippet | Some generalisations of the Preece theorem involving the product of two Kummer's functions 1F1 are obtained using Dixon's theorem and some well-known... Some generalisations of the Preece theorem involving the product of two Kummer's functions 1 F 1 are obtained using Dixon's theorem and some well-known... |
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| SubjectTerms | Dixon's theorem Hypergeometric functions Identities multiple Gaussian hypergeometric functions Preece's theorem Theorems |
| Title | Some multivariable Gaussian hypergeometric extensions of the Preece theorem |
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