SUMMATION FORMULAS DERIVED FROM THE SRIVASTAVA'S TRIPLE HYPERGEOMETRIC SERIES HC

Title & Authors
SUMMATION FORMULAS DERIVED FROM THE SRIVASTAVA'S TRIPLE HYPERGEOMETRIC SERIES HC
Kim, Yong-Sup; Rathie, Arjun Kumar; Choi, June-Sang;

Abstract
Srivastava noticed the existence of three additional complete triple hypergeometric functions $\small{H_A}$, $\small{H_B}$ and $\small{H_C}$ of the second order in the course of an extensive investigation of Lauricella's fourteen hypergeometric functions of three variables. In 2004, Rathie and Kim obtained four summation formulas containing a large number of very interesting reducible cases of Srivastava's triple hypergeometric series $\small{H_A}$ and $\small{H_C}$. Here we are also aiming at presenting two unified summation formulas (actually, including 62 ones) for some reducible cases of Srivastava's $\small{H_C}$ with the help of generalized Dixon's theorem and generalized Whipple's theorem on the sum of a $\small{_3F_2}$ obtained earlier by Lavoie et al.. Some special cases of our results are also considered.
Keywords
triple hypergeometric series $\small{H_A}$ and $\small{H_C}$;Appell's function;generalized Dixon's theorem;generalized Whipple's theorem;
Language
English
Cited by
References
1.
W. N. Bailey, Generalized Hypergeometric Series, Cambridge University Press, Cambridge, 1935.

2.
Y. S. Kim, A. K. Rathie, and J. Choi, Note on Srivastava's triple hypergeometric series \$H_A\$ and \$H_C\$, Commun. Korean Math. Soc. 18 (2003), no. 3, 581-586.

3.
G. Lauricella, Sulle funzioni ipergeometriche a piu variabli, Rend. Circ. Mat. Palermo 7 (1893), 111-158.

4.
J. L. Lavoie, F. Grondin, and A. K. Rathie, Generalizations of Watson's theorem on the sum of a \$_3F_2\$, Indian J. Math. 34 (1992), no. 1, 23-32.

5.
J. L. Lavoie, Generalizations of Whipple's theorem on the sum of a \$_3F_2\$, J. Comput. Appl. Math. 72 (1996), no. 2, 293-300.

6.
J. L. Lavoie, F. Grondin, A. K. Rathie, and K. Arora, Generalizations of Dixon's theorem on the sum of a \$_3F_2\$, Math. Comp. 62 (1994), no. 205, 267-276.

7.
A. K. Rathie and Y. S. Kim, Further results on Srivastava's triple hypergeometric series \$H_A\$ and \$H_C\$, Indian J. Pure Appl. Math. 35 (2004), no. 8, 991-1002.

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

9.
H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Ellis Horwood Ltd., Chichester, New York, 1984.