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Some multivariable Gaussian hypergeometric extensions of the Preece theorem

Published online by Cambridge University Press:  17 February 2009

M. I. Qureshi ,
M. Sadiq Khan ,
M. A. Pathan  and
N. U. Khan
M. I. Qureshi
Affiliation:
Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia, New Delhi-110025, India.
M. Sadiq Khan
Affiliation:
Department of Mathematics, Shibli National College, Paharpur, Azamgarh, U.P., India; e-mail: mohdsadiq786@rediffmail.com.
M. A. Pathan
Affiliation:
Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India; e-mail: mapathan@gmail.com, nabi-khan@rediffmail.com.
N. U. Khan
Affiliation:
Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India; e-mail: mapathan@gmail.com, nabi-khan@rediffmail.com.
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Abstract

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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.

Keywords

Dixon's theoremPreece's theoremmultiple Gaussian hypergeometric functions.
Type
Research Article
Information
The ANZIAM Journal , Volume 48 , Issue 1 , July 2006 , pp. 143 - 150
Copyright
Copyright © Australian Mathematical Society 2006

References

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