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ON AN EXTENSION FORMULAS FOR THE TRIPLE HYPERGEOMETRIC SERIES X8 DUE TO EXTON

  • Published : 2007.11.30
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Abstract

The aim of this article is to derive twenty five transformation formulas in the form of a single result for the triple hypergeometric series $X_8$ introduced earlier by Exton. The results are derived with the help of generalized Watson#s theorem obtained earlier by Lavoie et al. An interesting special cases are also pointed out.

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References

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  3. Y. S. Kim, J. Choi, and A. K. Rathie, Remark on two results by Padmanabham for Exton's triple hypergeometric series $X_8$, Honam Math. J. 27 (2005), no. 4, 603-608
  4. Y. S. Kim, J. Choi, and A. K. Rathie, Another method for Padmanabham's transformation formula for Exton's triple hypergeometric series $X_8$, submitted, Indian J. appl. Math
  5. J. L. Lavoie, F. Grondin, and A. K. Rathie, Generalizatons of Watson's theorem on the sum of a $_3F_2$, Indian J. Math. 34 (1992), no. 2, 23-32
  6. E. D. Rainville, Special functions, The Macmillan company, New York, 1960
  7. H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston, and London, 2001
  8. H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Ellis Harwood limited, Chichester, 1985
  9. H. M. Srivastava and H. L. Monacha, A Treatise on Generating Functions, Ellis Harwood limited, Chichester, 1984

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