arXiv subjects

Yashoverdhan Vyas

Publications and source records attributed to Yashoverdhan Vyas.

4 recordsLinked to original sources

arXiv2017

Extensions of the classical theorems for very well-poised hypergeometric functions

The classical summation and transformation theorems for very well-poised hypergeometric functions, namely, $_{5}F_4(1)$ summation, Dougall's $_{7}F_6(1)$ summation, Whipple's $_{7}F_6(1)$ to $_{4}F_3(1)$ transformation and Bailey's $_{9}F_8(1)$ to $_{9}F_8(1)$ transformation are extended. These extensions are derived by applying the well-known Bailey's transform method along with the classical very well-poised summation and transformation theorems for very well-poised hypergeometric functions and the Rakha and Rathie's extension of the Saalschütz's theorem. To show importance and applications of the discovered extensions, a number of special cases are pointed out, which leads not only to the extensions of other classical theorems for very well-poised and well-poised hypergeometric functions but also generate new hypergeometric summations and transformations.

math.CA↗

arXiv2016

On Some Expansion Theorems Involving Confluent Hypergeometric $_{2}F_{2}(x)$ Polynomial

Recently, Rathie and Kılıçman (2014) employed Kummer-type transformation for $_{2}F_{2}(a, d+1; b, d; x)$ to develop certain classes of expansions theorems for $_{2}F_{2}(x)$ hypergeometric polynomial. Our aim is to deduce Kummer-type transformation for $_{2}F_{2}(a, d+2; b, d; x)$ and utilize it to develop some new expansion theorems for the confluent hypergeometric $_{2}F_{2}(x)$ polynomial. We also obtain a well-known result given by Kim et al. (Integral Transforms Spec. Funct. 23(6); 435-444, 2012) and many other new results as particular cases of our theorems.

math.CA↗

arXiv2016

On transformation formulae for Srivastava-Daoust type $q$-hypergeometric series

We present here the $q$-analogues of certain transformations or reduction formulae for Srivastava-Daoust type double hypergeometric series. These reduction formulae are derived by utilizing the extended Bailey's Transform developed and studied by Joshi and Vyas [Int. J. Math. Sci., (12), 2005, 1909-1927]. A number of well-known $q$-hypergeometric transformations are also obtained as special cases of our results.

math.CA↗

arXiv2007

Bailey Type Transforms and Applications

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 $q$-hypergeometric identities, converting double or triple series into a very-well-poised $_{10}Φ_9$ or $_{12}Φ_{11}$ series but can also be utilized to derive new double and triple series Rogers-Ramanujan type identities and corresponding infinite families of Rogers-Ramanujan type identities.

math.CA↗