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This paper investigates an extended form Hurwitz-Lerch zeta function, as well as related integral images, ordinary and fractional derivatives, and series expansions, using the term extended beta function. We establish a connection between the extended Hurwitz-Lerch zeta function and the Laguerre polynomials. Furthermore, we present a probability distribution application of the extended Hurwitz-Lerch zeta function ζν,λδ,μ. Several results, both known and new, are shown to follow as special cases of our findings. [ABSTRACT FROM AUTHOR]

In this paper we suggest an enhanced Geraghty-type contractive mapping for examining the existence properties of classical nonlinear operators with or without prior degenerates. The nonlinear operators are proved to exist with the imposition of the Geraghty-type condition in a non-empty closed subset of complete metric spaces. To showcase some efficacies of the Geraghty-type condition, convergent rate and stability are deduced. The results are used to study some asymptotic properties of perturbed integral and hypergeometric operators. The results also extend and generalize some existing Geraghty-type conditions. [ABSTRACT FROM AUTHOR]

In this paper, we obtain an analytical solution for an unsolved definite integral RC(m; n) from a 1915 paper of Srinivasa Ramanujan. We obtain our solution using the hypergeometric approach and an infinite series decomposition identity. Also, we give some generalizations of Ramanujan's integral RC(m; n) defined in terms of the ordinary hypergeometric function 2F3 with suitable convergence conditions. Moreover as applications of our result we obtain nine new infinite summation formulas associated with the hypergeometric functions 0F1, 1F2 and 2F3. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish two general finite integral formulas involving the product of Galue type Struve functions and Srivastava's polynomials. The results are given in terms of generalized (Wright's) hypergeometric functions. These results are obtained with the help of finite integrals due to Oberhettinger and Lavoie-Trottier. Some interesting special cases of the main results are also considered. The results presented here are of general character and easily reducible to new and known integral formulae. [ABSTRACT FROM AUTHOR]

Motivated by the results on generating functions investigated by H. Exton and many other authors, we derive certain (presumably) new generating functions for generalized Mittag-Leffler-type functions. Specifically, we introduce a new class of generating relations (which are partly bilateral and partly unilateral) involving the generalized Mittag-Leffler function. Also we present some special cases of our main result. [ABSTRACT FROM AUTHOR]

A number of identities associated with the product of generalized hyper-geometric series have been investigated. In this paper, we aim to establish an identity involving the product of the generalized hypergeometric series 2F2. We do this using the generalized Kummer-type II transformation due to Rathie and Pogany and another identity due to Bailey. The result presented here, being general, can be reduced to a number of relatively simple identities involving the product of generalized hypergeometric series, some of which are observed to correspond to known ones. [ABSTRACT FROM AUTHOR]

In this paper, we present new generalized incomplete Pochhammer symbols and using this we introduce the extended generalized incomplete hypergeometric functions. We derive certain properties, generating functions and reduction formulas of these extended generalized incomplete hypergeometric functions. Special cases of this extended generalized incomplete hypergeometric functions are also discussed. [ABSTRACT FROM AUTHOR]

Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [30] and the second Appell function [6], we introduce here the incomplete Lauricella functions γ(n)A and Γ(n)A of n variables. We then systematically investigate several properties of each of these incomplete Lauricella functions including, for example, their various integral representations, finite summation formulas, transformation and derivative formulas, and so on. We provide relevant connections of some of the special cases of the main results presented here with known identities. Several potential areas of application of the incomplete hypergeometric functions in one and more variables are also pointed out. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of Mellin, Laplace, Euler and Whittaker transforms involving Struve function, generalized Wright function and Fox's H-function. The main results are presented in the form of four theorems. On account of the general nature of the functions involved here in, the main results obtained here yield a large number of known and new results in terms of simpler functions as their special cases. For the sake of illustration some corollaries have been recorded here as special cases of our main findings. [ABSTRACT FROM AUTHOR]

This paper continues the study of recursion formulas of multivariable hypergeometric functions. Earlier, in [4], the authors have given the recursion formulas for three variable Lauricella functions, Srivastava's triple hypergeometric functions and fc-variable Lauricella functions. Further, in [5], we have obtained recursion formulas for the general triple hypergeometric function. We present here the recursion formulas for Exton's triple hypergeometric functions. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce sufficient conditions for (Gaussian) hypergeometric functions to be in various subclasses of analytic functions. Also, we investigate several mapping properties involving these subclasses. [ABSTRACT FROM AUTHOR]

Several interesting and useful extensions of some familiar special functions such as Beta and Gauss hypergeometric functions and their properties have, recently, been investigated by many authors. Motivated mainly by those earlier works, we establish some fractional integral formulas involving the extended generalized Gauss hypergeometric function by using certain general pair of fractional integral operators involving Gauss hypergeometric function 2F1, Some interesting special cases of our main results are also considered. [ABSTRACT FROM AUTHOR]

Very recently the authors have obtained a very interesting reduction formula for the Srivastava's triple hypergeometric series F(3)(x, y, z) by applying the so-called Beta integral method to the Henrici's triple product formula for the hypergeometric series. In this sequel, we also present three more interesting reduction formulas for the function F(3)(x, y, z) by using the well known identities due to Bailey and Ramanujan. The results established here are simple, easily derived and (potentially) useful. [ABSTRACT FROM AUTHOR]

We aim at presenting certain unexpected functional relations among various hypergeometric functions of one or several variables (for example, see the identities in Corollary 5) by making use of Carlson's method employed in his work (Some extensions of Lardner's relations between 0F3 and Bessel functions, SIAM J. Math. Anal. 1(2)(1970), 232-242). [ABSTRACT FROM AUTHOR]

Differential subordination and superordination results are obtained for multivalent meromorphic functions associated with the Liu-Srivastava linear operator in the punctured unit disk. These results are derived by investigating appropriate classes of admissible functions. Sandwich-type results are also obtained. [ABSTRACT FROM AUTHOR]

In the present investigation, we introduce new classes of p-valent meromorphic functions defined by Liu-Srivastava linear operator and the multiplier transform and study their properties by using certain first order differential subordination and superordination. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to introduce a new subclass of meromorphic multivalent functions defined by using a linear operator associated with the generalized hypergeometric function. Some properties of this class are established here by using the principle of differential subordination and convolution in geometric function theory. [ABSTRACT FROM AUTHOR]

The aim of this paper is to evaluate four finite integrals involving the product of Srivastava's polynomials, a generalized hypergeometric function and H¯-function proposed by Inayat Hussian which contains a certain class of Feynman integrals. At the end, we give an application of our main findings by connecting them with the Riemann-Liouville type of fractional integral operator. The results obtained by us are basic in nature and are likely to find useful applications in several fields notably electric networks, probability theory and statistical mechanics. [ABSTRACT FROM AUTHOR]

The aim of this paper is to derive a fractional derivative of the multivariable H-function of Srivastava and Panda, associated with a general class of multivariable polynomials of Srivastava and the generalized Lauricella functions of Srivastava and Daoust. Certain special cases have also been discussed. The results derived here are of a very general nature and hence encompass several cases of interest hitherto scattered in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we derive some generating relations involving Konhauser polynomials, Gauss, Humbert, Appell and Kampé de Fériet hypergeometric functions with the help of four general theorems on generating functions (partly unilateral and partly bilateral) of one and two variables. [ABSTRACT FROM AUTHOR]

In this paper we consider generalizations of the classical Dixon's theorem and the classical Whipple's theorem on the sum of a 3F2. The results are derived with the help of generalized Watson's theorem obtained earlier by Mitra. A large number of results contiguous to Dixon's and Whipple's theorems obtained earlier by Lavoie, Grondin and Rathie, and Lavoie, Grondin, Rathie and Arora follow special cases of our main findings. [ABSTRACT FROM AUTHOR]

Applications of Weyl fractional q-integral operator to various generalized basic hypergeometric functions including the basic analogue of Fox's H-function have been investigated in the present paper. Certain interesting special cases have also been deduced. [ABSTRACT FROM AUTHOR]

Applications of Weyl fractional q-integral operator to various generalized basic hypergeometric functions including the basic analogue of Fox's H-function have been investigated in the present paper. Certain interesting special cases have also been deduced. [ABSTRACT FROM AUTHOR]