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In this article, generalized pathway integral operator with the classical Gauss hypergeometric function kernel and the fractional differential operators are used to studied new extended hypergeometric function. Furthermore, extended fractional kinetic equation involving new extended hypergeometric function that contained two Fox-Wright function as regularizer is investigated using Sumudu transform and Wiman's function. [ABSTRACT FROM AUTHOR]

The main object of this paper is to establish seven elliptical integrals associated with hypergeometric functions and suggest new way to compute their numerical values. The results presented in this article are presumably new and not present in the scientific literature. [ABSTRACT FROM AUTHOR]

In the present article, our main goal is to study the new extended beta, Gauss and confluent hypergeometric functions defined by using the two Fox-Wright functions as their kernel. Some applications of the new extended beta function to distribution theory are also discussed. [ABSTRACT FROM AUTHOR]

In this article, authors discussed about image formulas for the some new extended hypergeometric function using elementary properties of the fractional calculus integral operators. Furthermore, using integral transforms some image formulas are also established. [ABSTRACT FROM AUTHOR]

The main object of this paper is to present a family of -series identities which involve some of the theta functions of Jacobi and Ramanujan. Each of these (presumably new) -series identities reveals interesting relationships among three of the theta-type functions which stem from the celebrated Jacobi's triple-product identity in a remarkably simple way. The results presented in this paper are motivated essentially by a number of recent works dealing with the subject matter which is investigated herein. [ABSTRACT FROM AUTHOR]

We establish new functional relations for the dilogarithm involving two variables, which adhere the properties of Polylogarithm. We also considered several closely-related identities such as (for example) polylogarithm (also known as Jonqui`ere’s function), Euler dilogarithm function and Clausen’s function. [ABSTRACT FROM AUTHOR]

The main object of this paper is to present 6 new interrelationships between mock theta functions and combinatorial partition identities. The results presented in this paper are motivated by some recent works by M.P.Chaudhary. [ABSTRACT FROM AUTHOR]

In this paper, we give an extension of the first Heine's transformation formula using q-difference equations. Further, we discussed a Ramanujan's theta function ψ(q) and deduced it as a particular case. [ABSTRACT FROM AUTHOR]

The authors establish a set of fifteen new integral representations of Euler-type for the Sharma and Parihar hypergeometric function in four variables F(4)20; whose kernels include the quadruple functions K1;K10; F(4)14 and X(4)8; the Exton hypergeometric functions of three variables X4; the Lauricella functions of three variable FE; FN and FR; the Appell's series of two variables F2; F3 and F4; and the Gauss hypergeometric function. [ABSTRACT FROM AUTHOR]

The main purpose of this article is to prove two Rogers–Ramanujan–Slater type theta function identities related to φ(q) and ϕ0(q), which were earlier investigated by two legendary mathematicians of their time. The results presented in this paper are motivated essentially by recent works of Cao et al. (see [5]). [ABSTRACT FROM AUTHOR]

In this paper, we research theta function identity involving Rogers–Ramanujan identity and establish a Rogers–Ramanujan–Slater type theta function identity related to G(q) and φ(q). [ABSTRACT FROM AUTHOR]

The aim of this research paper is to establish fifty new class of integrals involving hypergeometric function in terms of gamma functions. In order to put these fifty integrals, two master formulas have been constructed. The results are derived with the help of an interesting integral due to Lavoie and Trottier and generalized Watson's summation theorem obtained earlier by the Lavoie, Grondhi and Rathi. More than hundred interesting special cases (and four very special results) have also been obtained from our main results. [ABSTRACT FROM AUTHOR]