SUMMATION FORMULAS DERIVED FROM THE SRIVASTAVA`S TRIPLE HYPERGEOMETRIC SERIES HC Kim, Yong-Sup; Rathie, Arjun Kumar; Choi, June-Sang;
Srivastava noticed the existence of three additional complete triple hypergeometric functions , and 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 and . Here we are also aiming at presenting two unified summation formulas (actually, including 62 ones) for some reducible cases of Srivastava`s with the help of generalized Dixon`s theorem and generalized Whipple`s theorem on the sum of a obtained earlier by Lavoie et al.. Some special cases of our results are also considered.
triple hypergeometric series and ;Appell`s function;generalized Dixon`s theorem;generalized Whipple`s theorem;
W. N. Bailey, Generalized Hypergeometric Series, Cambridge University Press, Cambridge, 1935.
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.
G. Lauricella, Sulle funzioni ipergeometriche a piu variabli, Rend. Circ. Mat. Palermo 7 (1893), 111-158.
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.
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.
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.
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.
H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, 2001.
H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Ellis Horwood Ltd., Chichester, New York, 1984.