Generalization of two theorems due to Ramanujan

Yong S. Kim, Arjun K. Rathie, Richard B. Paris

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)314-323
Number of pages10
JournalIntegral Transforms and Special Functions
Volume24
Issue number4
Early online date24 May 2012
DOIs
Publication statusPublished - 2013

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Ramanujan
Theorem
Gauss Hypergeometric Function
Derivatives
Summation
Gauss
Non-negative
Derivative
Integer
Generalization

Cite this

Kim, Yong S. ; Rathie, Arjun K. ; Paris, Richard B. / Generalization of two theorems due to Ramanujan. In: Integral Transforms and Special Functions. 2013 ; Vol. 24, No. 4. pp. 314-323.
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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 journalArticle

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