Abstract
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.
Original language | English |
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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 |
Keywords
- Hypergeometric series
- Generalized Gauss summation theorem
- Ramanujan's sum
- Sums of Hermite polynomials