### Abstract

*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 |
---|---|

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

*Integral Transforms and Special Functions*,

*24*(4), 314-323. https://doi.org/10.1080/10652469.2012.689302

}

*Integral Transforms and Special Functions*, vol. 24, no. 4, pp. 314-323. https://doi.org/10.1080/10652469.2012.689302

**Generalization of two theorems due to Ramanujan.** / Kim, Yong S.; Rathie, Arjun K.; Paris, Richard B.

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 -