ANOTHER METHOD FOR PADMANABHAM'S TRANSFORMATION FORMULA FOR EXTON'S TRIPLE HYPERGEOMETRIC SERIES X8

Title & Authors
ANOTHER METHOD FOR PADMANABHAM'S TRANSFORMATION FORMULA FOR EXTON'S TRIPLE HYPERGEOMETRIC SERIES X8
Kim, Yong-Sup; Rathie, Arjun Kumar; Choi, June-Sang;

Abstract
The object of this note is to derive Padmanabham's transformation formula for Exton's triple hypergeometric series $\small{X_8}$ by using a different method from that of Padmanabham's. An interesting special case is also pointed out.
Keywords
triple hypergeometric series $\small{X_8}$;Horn functions;Laplace integral;Srivastava and Panda's function;Dixon's summation theorem for $\small{_3F_2(1)}$;
Language
English
Cited by
1.
CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION \$X_2\$,;;;

한국수학교육학회지시리즈B:순수및응용수학, 2010. vol.17. 4, pp.347-354
2.
CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X5,;;;

호남수학학술지, 2010. vol.32. 3, pp.389-397
3.
AN EXTENSION OF THE TRIPLE HYPERGEOMETRIC SERIES BY EXTON,;;

호남수학학술지, 2010. vol.32. 1, pp.61-71
4.
GENERALIZED DOUBLE INTEGRAL INVOLVING KAMPÉ DE FÉRIET FUNCTION,;;;

호남수학학술지, 2011. vol.33. 1, pp.43-50
5.
DECOMPOSITION FORMULAS AND INTEGRAL REPRESENTATIONS FOR SOME EXTON HYPERGEOMETRIC FUNCTIONS,;;;

충청수학회지, 2011. vol.24. 4, pp.745-758
6.
GENERALIZED SINGLE INTEGRAL INVOLVING KAMP\$\acute{E}\$ DE F\$\acute{E}\$RIET FUNCTION,;;;

충청수학회지, 2011. vol.24. 2, pp.205-212
7.
Generalization of a Transformation Formula for the Exton's Triple Hypergeometric Series X12 and X17,;;

Kyungpook mathematical journal, 2014. vol.54. 4, pp.677-684
1.
CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X5, Honam Mathematical Journal, 2010, 32, 3, 389
2.
AN EXTENSION OF THE TRIPLE HYPERGEOMETRIC SERIES BY EXTON, Honam Mathematical Journal, 2010, 32, 1, 61
3.
Generalization of a Transformation Formula for the Exton's Triple Hypergeometric Series X12and X17, Kyungpook mathematical journal, 2014, 54, 4, 677
4.
CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X8, Communications of the Korean Mathematical Society, 2012, 27, 2, 257
5.
Relations between Lauricella’s triple hypergeometric function FA(3)(x,y,z) and Exton’s function X8, Advances in Difference Equations, 2013, 2013, 1, 34
6.
GENERALIZED DOUBLE INTEGRAL INVOLVING KAMPÉ DE FÉRIET FUNCTION, Honam Mathematical Journal, 2011, 33, 1, 43
References
1.
P. Appell et J. Kampe de Feriet, Fonctions Hypergeometriques et Hypersph´eriques Polynomes D'Hermite, Gauthier-Villars, Paris, 1926

2.
J. Choi, Notes on formal manipulations of double series, Commun. Korean Math. Soc. 18 (2003), no. 4, 781–789

3.
H. Exton, Hypergeometric function of three variables, J. Indian Acad. Maths. 4 (1982), no. 2, 113–119

4.
G. H. Hardy, A chapter from Ramanujan's notebook, Proc. Cambridge Philos. Soc. 21 (1923), 492–503

5.
J. Kampe de Feriet, Les fonctions hypergeometriques dordre superieur a deux variables, C. R. Acad. Sci. Paris 173 (1921), 401–404

6.
P. A. Padmanabham, Expansions for a multiple hypergeometric function, Ganita 54 (2003), no. 1, 17–20

7.
C. T. Preece, The product of two generalized hypergeometric functions, Proc. London Math. Soc. 22 (1924), 370–380

8.
H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston, and London, 2001

9.
H. M. Srivastava and P. W. Karlsson, Multiple Gaussian Hypergeometric Series, Halsted Press (Ellis Horwood Limited, Chichester); Wiley, New York, Chichester, Brisbane, and Toronto, 1985

10.
H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester); Wiley, New York, Chichester, Brisbane, and Toronto, 1984

11.
H. M. Srivastava and R. Panda, An integral representation for the product of two Jacobi polynomials, J. London Math. Soc. 12 (1976), no. 2, 419–425