Related papers: The integral Mittag-Leffler, Whittaker and Wright …

By means of inversion techniques and several known hypergeometric series identities, summation formulas for Fox-Wright function are explored. They give some new hypergeometric series identities when the parameters are specified.

We present a method using contour integration to derive definite integrals and their associated infinite sums which can be expressed as a special function. We give a proof of the basic equation and some examples of the method. The advantage…

Geometric generalized Mittag-Leffler distributions having the Laplace transform $\frac{1}{1+\beta\log(1+t^\alpha)},0<\alpha\le 2,\beta>0$ is introduced and its properties are discussed. Autoregressive processes with Mittag-Leffler and…

An integral formula is developed which applies to an essentially arbitrary function. An application is made to the Riemann zeta function.

Using Cauchy's Integral Theorem as a basis, what may be a new series representation for Dirichlet's function $\eta(s)$, and hence Riemann's function $\zeta(s)$, is obtained in terms of the Exponential Integral function $E_{s}(i\kappa)$ of…

The definitions and main properties of the Ihara and Bartholdi zeta functions for infinite graphs are reviewed. The general question of the validity of a functional equation is discussed, and various possible solutions are proposed.

We introduce the linear operators of fractional integration and fractional differentiation in the framework of the Riemann-Liouville fractional calculus. Particular attention is devoted to the technique of Laplace transforms for treating…

We introduce a new factorial function which agrees with the usual Euler gamma function at both the positive integers and at all half-integers, but which is also entire. We describe the basic features of this function.

In this paper we find fractional Riemann-Liouville derivatives for the Takagi-Landsberg functions. Moreover, we introduce their generalizations called weighted Takagi-Landsberg functions which have arbitrary bounded coefficients in the…

Product-to-sum identities for trigonometric functions play a fundamental role in function theory and numerous applications. In this spirit, we present convolution-to-sum identities for Mittag-Leffler type functions. Using a Laplace domain…

We utilize a combination of integral transforms, including the Laplace transform, with some classical results in analytic number theory concerning the Riemann $\xi$-function, to obtain a new integral equation. We also provide a new proof of…

This paper is devoted for the study of a new generalization of Struve function type. In this paper , We establish four new integral formulas involving the Galue type Struve function, which are express in term of the generalized (Wright)…

In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…

This paper deals with a Euler type integral operator involving k-Mittag-Leffler function defined by Gupta and Parihar [8]. Furthermore, some special cases are also taken into consideration.

The variable change w=exp(u) is applied to establish novel integral representations of the incomplete gamma-function, hypergeometric F-function,confluent hypergeometric /Phi-function and beta-function, and to analyze these functionsas as…

Inspired by certain interesting recent extensions of the gamma, beta and hypergeometric matrix functions, we introduce here new extension of the gamma and beta matrix function. We also introduce new extensions of the Gauss hypergeometric…

We have established novel integral representations of the Riemann zeta-function and Dirichlet eta-function based on powers of trigonometric functions and digamma function, and then use these representations to find close forms of Laurent…

The object of this paper is to investigate the certain results involving Bateman's matrix polynomials for integral index. We obtain some properties, integral representation and recurrence relations for hypergeometric matrix function. We…

This mostly expository article explores recent developments in the relations between the three objects in the title from an algebro-combinatorial perspective. We prove a formula for Whittaker functions of a real semisimple group as an…

In this paper, we first introduce certain forms of extended incomplete Pochhammer symbols which are then used to define families of extended incomplete generalized hypergeometric functions. For these functions, we investigate various…