On extensions of two results due to Ramanujan | Zendy

Y. S. Kim | Zendy; Arjunkumar RATHIE | Zendy; R. B. Paris | Zendy

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On extensions of two results due to Ramanujan

Author(s) -

Y. S. Kim,

Arjunkumar RATHIE,

R. B. Paris

Publication year - 2019

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1909-59

Subject(s) - ramanujan's sum , mathematics , generalization , hypergeometric function , pure mathematics , argument (complex analysis) , function (biology) , basic hypergeometric series , generalized hypergeometric function , algebra over a field , mathematical analysis , biochemistry , chemistry , evolutionary biology , biology

The aim in this note is to provide a generalization of an interesting entry in Ramanujan’s Notebooks that relate sums involving the derivatives of a function (t) evaluated at 0 and 1. The generalization obtained is derived with the help of expressions for the sum of terminating 3F2 hypergeometric functions of argument equal to 2, recently obtained in Kim et al. [Two results for the terminating 3F2(2) with applications, Bull. Korean Math. Soc. 49 (2012) pp. 621–633]. Several special cases are given. In addition we generalize a summation formula to include integral parameter differences.

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