Abstract
| Original language | English |
|---|---|
| Pages (from-to) | 314-323 |
| Number of pages | 10 |
| Journal | Integral Transforms and Special Functions |
| Volume | 24 |
| Issue number | 4 |
| Early online date | 24 May 2012 |
| DOIs | |
| Publication status | Published - 2013 |
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Generalization of two theorems due to Ramanujan. / Kim, Yong S.; Rathie, Arjun K.; Paris, Richard B.
In: Integral Transforms and Special Functions, Vol. 24, No. 4, 2013, p. 314-323.Research output: Contribution to journal › Article
TY - JOUR
T1 - Generalization of two theorems due to Ramanujan
AU - Kim, Yong S.
AU - Rathie, Arjun K.
AU - Paris, Richard B.
PY - 2013
Y1 - 2013
N2 - The aim in this paper is to provide generalizations of two interesting entries in Ramanujan's notebooks that relate sums involving the derivatives of a function φ(t) evaluated at 0 and 1. The generalizations obtained are derived with the help of expressions for the Gauss hypergeometric function 2 F 1(−n, a; 2a+j; 2) for non-negative integer n and j=0,±1, …,±5 given very recently by Kim et al. [Generalizations of Kummer's second theorem with applications, Comput. Math. Math. Phys. 50(3) (2010), pp. 387–402] and extension of Gauss’ summation theorem available in the literature. Several special cases that are closely related to Ramanujan's results are also given.
AB - The aim in this paper is to provide generalizations of two interesting entries in Ramanujan's notebooks that relate sums involving the derivatives of a function φ(t) evaluated at 0 and 1. The generalizations obtained are derived with the help of expressions for the Gauss hypergeometric function 2 F 1(−n, a; 2a+j; 2) for non-negative integer n and j=0,±1, …,±5 given very recently by Kim et al. [Generalizations of Kummer's second theorem with applications, Comput. Math. Math. Phys. 50(3) (2010), pp. 387–402] and extension of Gauss’ summation theorem available in the literature. Several special cases that are closely related to Ramanujan's results are also given.
U2 - 10.1080/10652469.2012.689302
DO - 10.1080/10652469.2012.689302
M3 - Article
VL - 24
SP - 314
EP - 323
JO - Integral Transforms and Special Functions
JF - Integral Transforms and Special Functions
SN - 1065-2469
IS - 4
ER -