ANZIAM  J.  48 (2006), 143-150
Some multivariable Gaussian hypergeometric extensions of the Preece theorem

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


Abstract
Some generalisations of the Preece theorem involving the product of two Kummer's functions ${}_1F_1$ 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 $F_p^{(4)}$ 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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