Abdul Hakim Khan

On Some Properties of a Generalization of Bessel-Maitland Function

The present paper is the investigation of certain properties of generalized Bessel-Maitland function, written in the form ࡶ ࣇ ,ࢗ ࣆ ,ࢽ (ࢠ ) = ∑ � ஶ ࢔ୀ૙ (ࢽ )ࢗ࢔ (ࢠ )࢔ ࢔ !ડ (ࣆ࢔ ାࣇା૚ ) , where ࣆ ,ࣇ ,ࢽ∈ ࡯ ;ࡾࢋ (ࣆ ) ≥ ૙ , ࡾࢋ (ࣇ ) ≥ −૚ ,ࡾࢋ (ࢽ ) ≥ ૙ and ࢗ∈ (૙ ,૚ )∪ ࡺ. For the function ࡶ ࣇ ,ࢗ ࣆ ,ࢽ (ࢠ ) , a number of results including differentiation and integration formulas, Mellin-Barnes integral representation, Laplace transform, Euler transform, ࢑ -transform, Varma transform, Mellin transform. Various relationship with other functions including Foxs ࡴ-function and Wright hypergeometric function were also established. In the end certain relations have been obtained by using the Riemann-Liouville fractional integrals and derivatives.

Some New Results Associated with the Generalized Lommel-Wright Function

The aim of this article is to establish a new class of unified integrals associated with the generalized Lommel-Wright functions, which are expressed in terms of Wright Hypergeometric function.Some integrals involving trigonometric,generalized Bessel function and Struve functions are also indicated as special cases of our main results.further, with the help of our main results and their special cases, we obtain two reduction formulas for the Wright hypergeometric function. keywords: Gamma function, generalized Wright hypergeometric function pψq, Hypergeometric function pFq, generalized Lommel-Wright functions J μm ν,λ (z), Lavoie-Trottier integral formula. MSC[2010]: 33B20, 33C20, 33B15

ON SOME GENERATING FUNCTIONS OF GENERALIZED BATEMAN'S AND PASTERNAK'S POLYNOMIALS OF TWO VARIABLES

The aim of the present paper is to study some generating functions of generalized Batemans and Pasternaks polynomials of two variables.

A note on Hermite polynomials of several variables

The present paper deals with an extension of certain results obtained by Burchnall for Hermite polynomials to similar results for Hermite polynomials of several variables.

Triple generating functions of Jacobi polynomials of two variables

The present paper is a study of triple generating functions of Jacobi polynomials of two variables.

BILINEAR AND BILATERAL GENERATING FUNCTIONS OF HEAT TYPE POLYNOMIALS SUGGESTED BY JACOBI POLYNOMIALS

The present paper deals with generalization of several families of bilinear and bilateral generating functions for the heat type polynomials suggested by Jacobi polynomials with different argument.