ON SUMS OF CERTAIN CLASSES OF SERIES

Title & Authors
ON SUMS OF CERTAIN CLASSES OF SERIES
Kim, Yong-Sup; Chaudhary, Mahendra Pal; Rathie, Arjun Kumar;

Abstract
The aim of this research note is to provide the sums of the series $\small{\sum_{k=0}^{\infty}(-1)^k$${{a-i}\atop{k}}$$\frac{1}{2^k(a+k+1)}}$ for $\small{i}$ = 0, $\small{{\pm}1}$,$\small{{\pm}2}$,$\small{{\pm}3}$,$\small{{\pm}4}$,$\small{{\pm}5}$. The results are obtained with the help of generalization of Bailey's summation theorem on the sum of a $\small{_2F_1}$ obtained earlier by Lavoie et al.. Several interesting results including those obtained earlier by Srivastava, Vowe and Seiffert, follow special cases of our main findings. The results derived in this research note are simple, interesting, easily established and (potentially) useful.
Keywords
Bailey's summation theorem;summation theorems;gamma function;
Language
English
Cited by
References
1.
J. Choi, Peter Zoring, and A. K. Rathie, Sums of certain classes of series, Comm. Korean Math. Soc. 14 (1999), no. 3, 641-647.

2.
E. E. Kummer, Uber die hypergeometrische Reihe, J. Reine Angew. Math. 15 (1836), 39-83; 127-172.

3.
J. L. Lavoie, F. Grondin, and A. K. Rathie, Generalizations of Whipple's theorem on the sum of a $_{3}F_{2}$, J. Comput. Appl. Math. 72 (1996), no. 2, 293-300.

4.
E. D. Rainville, Special Functions, The Macmillan Company, New York, 1960.

5.
H. M. Srivastava, Sums of a certain family of series, Elem. Math. 43 (1988), no. 2, 54-58.

6.
M. Vowe and H. J. Seiffert, Aufgabe 946, Elem. Math. 42 (1987), 111-112.