JOURNAL BROWSE
Search
Advanced SearchSearch Tips
GENERALIZATIONS OF TWO SUMMATION FORMULAS FOR THE GENERALIZED HYPERGEOMETRIC FUNCTION OF HIGHER ORDER DUE TO EXTON
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
GENERALIZATIONS OF TWO SUMMATION FORMULAS FOR THE GENERALIZED HYPERGEOMETRIC FUNCTION OF HIGHER ORDER DUE TO EXTON
Choi, June-Sang; Rathie, Arjun Kumar;
  PDF(new window)
 Abstract
In 1997, Exton, by mainly employing a widely-used process of resolving hypergeometric series into odd and even parts, obtained some new and interesting summation formulas with arguments 1 and -1. We aim at showing how easily many summation formulas can be obtained by simply combining some known summation formulas. Indeed, we present 22 results in the form of two generalized summation formulas for the generalized hypergeometric series , including two Exton's summation formulas for as special cases.
 Keywords
generalized hypergeometric series ;summation theorems for ;
 Language
English
 Cited by
 References
1.
J. Choi and H. M. Srivastava, Certain classes of infinite series, Monatsh. Math. 127 (1999), no. 1, 15–25. crossref(new window)

2.
W. Chu and L. de Donno, Hypergeometric series and harmonic number identities, Adv. in Appl. Math. 34 (2005), no. 1, 123–137. crossref(new window)

3.
H. Exton, Multiple Hypergeometric Functions and Applications, Ellis Horwood, Chichester, UK, 1976.

4.
H. Exton, Some new summation formulae for the generalised hypergeometric function of higher order, J. Comput. Appl. Math. 79 (1997), no. 2, 183–187. crossref(new window)

5.
J. L. Lavoie, F. Grondin, and A. K. Rathie, Generalizations of Whipple’s theorem on the sum of a $_3F_2$, J. Comput. Appl. Math. 72 (1996), no. 2, 293–300. crossref(new window)

6.
E. D. Rainville, Special Functions, The Macmillan Company, New York, 1960.

7.
L.-C. Shen, Remarks on some integrals and series involving the Stirling numbers and ${\zeta}(n)$, Trans. Amer. Math. Soc. 347 (1995), no. 4, 1391–1399. crossref(new window)

8.
L. J. Slater, Generalized Hypergeometric Functions, Cambridge University Press, Cambridge, 1966.

9.
H. M. Srivastava and J. Choi, Series Associated with the Zeta and Related Functions, Kluwer Academic Publishers, Dordrecht, Boston, and London, 2001.