Gasper followed the fractional calculus proof of an Erdélyi integral to derive its discrete
analogue in the form of a hypergeometric expansion. To give an alternative proof, we derive …

This paper provides three classes of q-summation formulas in the form of general
contiguous extensions of the first q-Kummer summation theorem. Their derivations are …

The well-known classical summation theorems due to Dougall and certain transformation
formulas due to Whipple and Bailey for very well-poised hypergeometric functions are …

The aim of this paper is to establish new series transforms of Bailey type and to show that
these Bailey type transforms work as efficiently as the classical one and give not only new …

The present paper aims to derive summation and transformation formulae for the
generalized very well-poised hypergeometric functions 2q+ 5F2q+ 4 (1) and 2q+ 7F2q+ 6 …

The generalized hypergeometric functions of one, two and more variables and allied Special
Functions, and their associated transformations, reductions and summations are potentially …

Recently, Vyas et al. have developed an alternative way of proof for the Gasper's discrete
analogue of an Erdélyi integral and inspired from this new type of derivation they resolved …

Over the years, the study of Bailey transform, Bailey lemma, Bailey pair, their variants and
their applications are the major subjects of interest. Of course, it is due to the efficiency of the …

In this paper, we derive two most general possible q-hypergeometric expansion formulae for
12Φ11 (q) and rΦs (z), respectively. The results are unique in the sense that no such results …

This transformation leads to various results which play an important role in number theory
and transformation theory of ordinary and basic hypergeometric series both. Making use of …