On a new class of series identities

The aim of this paper is to provide a new class of series identities in the form of four general results. The results are established with the help of generalizatons of the classical Kummers summation theorem obtained earlier by Rakha and Rathie. Results obtained earlier by Srivastava, Bailey and Rathie et al. follow special cases of our main findings.

A note on a generalization of two well-known Cominatorial identities via a Hypergeometric series approach

In this note, we aim to provide generalizations of (i) Knuths old sum (or Reed Dawson identity) and (ii) Riordans identity using a hypergeometric series approach.

Further summation formulas for the Kampe de Feriet function

The aim of this research is to provide thirty-two interesting summation formulas for the Kampe de Feriet function in general forms, which are given in sixteen theorems. The results are established with the help of the identities in Liu and Wang cite{Li-Wa} and generalizations of Kummers summation theorem, Gauss second summation theorem and Baileys summation theorem obtained earlier by Rakha and Rathie cite{Ra-Ra}. Some special cases and relevant connections of the results presented here with those involving certain known identities are also indicated.

On an identity for H-function

The main objective of this research note is to provide an identity for the H-function, which generalizes two identities involving H-function obtained earlier by Rathie and Rathie et al.

On a new identity for the H-function with applications to the summation of hypergeometric series

Using generalized hypergeometric functions to perform symbolic manipulation of equations is of great importance to pure and applied scientists. There are in the literature a great number of identities for the Meijer-G function. On the other hand, when more complex expressions arise, the latter function is not capable of representing them. The H-function is an alternative to overcome this issue, as it is a generalization of the Meijer-G function. In the present paper, a new identity for the H-function is derived. In short, this result enables one to split a particular H-function into the sum of two other H-functions. The new relation in addition to an old result are applied to the summation of hypergeometric series. Finally, some relations between H-functions and elementary functions are built

Comment on a paper Watson - like Formulae for terminating $_{3}F_2$ series by Chu and Zhou

In a recent paper, Chu and Zhou [Advances in Combinatorics, I.S. Kotsireas and E.V. Zima(eds.), 139-159 (2013)] established in all 40 closed formulae for terminating Watson-like hypergeometric $_{3}F_2$- series by investigating through Gould and Hsus fundamental pair of inverse series relations, the dual relations of Dougalls formula for the very well - poised $_{5}F_4$ - series. The aim of this short note is just to point out that out of 40 results, 33 results have already been discovered in 1992 by Lavoie, et al.

A new proof of the fundamental two-term transformation for the series ${}_3F_2(1)$ due to Thomae

The aim of this short note is to provide a very simple proof for obtaining the fundamental two-term transformation for the series ${}_3F_2(1)$ due to Thomae.

Another Method for Proving a Hypergeometric Generating relation contiguous to that of Exton

The aim of this note is to establish an interesting hypergeometric generating relation contiguous to that of Exton by a short method.