JOURNAL BROWSE
Search
Advanced SearchSearch Tips
ON A NEW CLASS OF SERIES IDENTITIES
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Honam Mathematical Journal
  • Volume 37, Issue 3,  2015, pp.339-352
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2015.37.3.339
 Title & Authors
ON A NEW CLASS OF SERIES IDENTITIES
SHEKHAWAT, NIDHI; CHOI, JUNESANG; RATHIE, ARJUN K.; PRAKASH, OM;
  PDF(new window)
 Abstract
We aim at giving explicit expressions of , where i = 0, , , and is a bounded sequence of complex numbers. The main result is derived with the help of the generalized Kummer's summation theorem for the series obtained earlier by Choi. Further some special cases of the main result considered here are shown to include the results obtained earlier by Kim and Rathie and the identity due to Bailey.
 Keywords
Gamma function;Pochhammer symbol;Hypergeometric function;Generalized hypergeometric function;Generalized Kummer's summation theorem;
 Language
English
 Cited by
 References
1.
W. N. Bailey, Product of generalized hypergeometric series, Proc. London Math. Soc. 228 (1928), 242-254.

2.
W. N. Bailey, Generalized Hypergeometric Series, Cambridge University Press, Cambridge (1935); Reprinted by Stechert Hafner, New York (1964).

3.
J. Choi, Contiguous extensions of Dixon's theorem on the sum of a $_3F_2$, J. Inequal. Appl. 2010 (2010), Article ID 589618.

4.
Y. S. Kim and A. K. Rathie, Application of generalized Kummer's summation theorem for the series $_2F_1$, Bull. Koreon Math. Soc. 46(6) (2009), 1201-1211. crossref(new window)

5.
J. L. Lavoie, F. Grondin, and A. K. Rathie, Generalization of Whipple's theorem on the sum of a $_3F_2$, J. Comput. Appl. Math. 72(2) (1996), 293-300. crossref(new window)

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

7.
H. M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, Amsterdam, London and New York, 2012.