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

• Kim, Yong-Sup (DEPARTMENT OF MATHEMATICS EDUCATION WONKWANG UNIVERSITY) ;
• Rathie, Arjun K. (DEPARTMENT OF MATHEMATICS GOVT. SUJANGARH COLLEGE)
• Published : 2007.11.30
• 83 5

#### 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.

#### Keywords

triple hypergeometric series $X_8$;laplace integral;$Kamp\acute{e}\;de\;F\acute{e}riet$ function;generalized Watson's theorem;the identities of Pochhammer symbol

#### References

1. W. N. Bailey, Generalized Hypergeometric series, Cambridge Tracts in Mathematics and Mathematical Physics, No. 32, Stechert-Hafner, Inc., New York 1964
2. H. Exton, Hypergeometric functions of three variables, J. Indian Acad. Math. 4 (1982), no. 2, 113-119
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. 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
5. E. D. Rainville, Special functions, The Macmillan company, New York, 1960
6. H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston, and London, 2001
7. H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Ellis Harwood limited, Chichester, 1985
8. H. M. Srivastava and H. L. Monacha, A Treatise on Generating Functions, Ellis Harwood limited, Chichester, 1984
9. 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

#### Cited by

1. APPLICATIONS OF GENERALIZED KUMMER'S SUMMATION THEOREM FOR THE SERIES2F1 vol.46, pp.6, 2009, https://doi.org/10.4134/BKMS.2009.46.6.1201
2. GENERALIZED DOUBLE INTEGRAL INVOLVING KAMPÉ DE FÉRIET FUNCTION vol.33, pp.1, 2011, https://doi.org/10.5831/HMJ.2011.33.1.043
3. AN EXTENSION OF THE TRIPLE HYPERGEOMETRIC SERIES BY EXTON vol.32, pp.1, 2010, https://doi.org/10.5831/HMJ.2010.32.1.061
4. ON CERTAIN REDUCIBILITY OF KAMPE DE FERIET FUNCTION vol.31, pp.2, 2009, https://doi.org/10.5831/HMJ.2009.31.2.167
5. Generalization of a Transformation Formula for the Exton's Triple Hypergeometric Series X12and X17 vol.54, pp.4, 2014, https://doi.org/10.5666/KMJ.2014.54.4.677
6. Contiguous Extensions of Dixon's Theorem on the Sum of a 3F2 vol.2010, 2010, https://doi.org/10.1155/2010/589618
7. CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X5 vol.32, pp.3, 2010, https://doi.org/10.5831/HMJ.2010.32.3.389
8. Relations between Lauricella’s triple hypergeometric function FA(3)(x,y,z) and Exton’s function X8 vol.2013, pp.1, 2013, https://doi.org/10.1186/1687-1847-2013-34
9. CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X8 vol.27, pp.2, 2012, https://doi.org/10.4134/CKMS.2012.27.2.257