FINITE INTEGRAL FORMULA INVOLVING ALEPH–FUNCTION AND GENERALIZED MITTAG–LEFFLER FUNCTION

On Integral Operator Involving Generalized Hypergeometric Function

Due to rigorous work on integral operators and the hypergeomet-ric functions, we define here an integral operator involving generalized hypergeometric function. By means of this generalized function, we introduce new classes of analytic functions and study their properties. 1 Introduction and preliminaries. Let H be the class of functions analytic in U := {z ∈ C : |z| < 1} and A be the subclass...

Beta Type Integral Formula Associated with Wright Generalized Bessel Function

Abstract. The object of the present paper is to establish an integral formula involving Wright generalized Bessel function (or generalized Bessel-Maitland function) J ν,q (z) defined by Singh et al. [21], which is expressed in the terms of generalized (Wright) hypergeometric functions. Some interesting special cases involving Bessel functions, generalized Bessel functions, generalized Mittag-Le...

On certain fractional calculus operators involving generalized Mittag-Leffler function

The object of this paper is to establish certain generalized fractional integration and differentiation involving generalized Mittag-Leffler function defined by Salim and Faraj [25]. The considered generalized fractional calculus operators contain the Appell's function $F_3$ [2, p.224] as kernel and are introduced by Saigo and Maeda [23]. The Marichev-Saigo-Maeda fractional calculus operators a...

An Integral Formula for Generalized Gegenbauer Polynomials and Jacobi Polynomials

A Finite Double Integral Involving Biorthogonal Polynomial, A Multivariable General Class of Polynomial and H - Function

In the present paper, we evaluate a finite double integral involving product of biorthogonal polynomial, a multivariable general class of polynomial and the H function with general arguments. The integral evaluated is quite general in nature and yields number of known and new integrals as its special cases. Several new interesting integrals of our findings have also been mentioned briefly.