### 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*; 2*a*+*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 |

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## Cite this

Kim, Y. S., Rathie, A. K., & Paris, R. B. (2013). Generalization of two theorems due to Ramanujan.

*Integral Transforms and Special Functions*,*24*(4), 314-323. https://doi.org/10.1080/10652469.2012.689302