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4 papers · 1 filter
On extensions of two results due to Ramanujan
Y. S. Kim, A. K. Rathie, R. B. Paris
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 Phi(t) evaluated at 0…
An alternative proof of the extended Saalschutz summation theorem for the r+3Fr+2(1) series with applications
Y. S. Kim, Arjun K. Rathie, R. B. Paris
A simple proof of a new summation formula for a terminating r+3Fr+2(1) hypergeometric series, representing an extension of Saalschutz's formula for a 3F2(1) series, is given for t…
A note on a series containing the Laguerre polynomials
Y. S. Kim, A. K. Rathie, R. B. Paris
Expressions for the summation of a new series involving the Laguerre polynomials are obtained in terms of generalized hypergeometric functions. These results provide alternative, a…
On two Thomae-type transformations for hypergeometric series with integral parameter differences
Y. S. Kim, Arjun. K. Rathie, R. B. Paris
We obtain two new Thomae-type transformations for hypergeometric series with r pairs of numeratorial and denominatorial parameters differing by positive integers. This is achieved…