THE INTEGRAL EXPRESSION INVOLVING THE FAMILY OF LAGUERRE POLYNOMIALS AND BESSEL FUNCTION

Title & Authors
THE INTEGRAL EXPRESSION INVOLVING THE FAMILY OF LAGUERRE POLYNOMIALS AND BESSEL FUNCTION
Shukla, Ajay Kumar; Salehbhai, Ibrahim Abubaker;

Abstract
The principal aim of the paper is to investigate new integral expression $\small{{\int}_0^{\infty}x^{s+1}e^{-{\sigma}x^2}L_m^{(\gamma,\delta)}\;({\zeta};{\sigma}x^2)\;L_n^{(\alpha,\beta)}\;({\xi};{\sigma}x^2)\;J_s\;(xy)\;dx}$, where $\small{y}$ is a positive real number; $\small{\sigma}$, $\small{\zeta}$ and $\small{\xi}$ are complex numbers with positive real parts; $\small{s}$, $\small{\alpha}$, $\small{\beta}$, $\small{\gamma}$ and $\small{\delta}$ are complex numbers whose real parts are greater than -1; $\small{J_n(x)}$ is Bessel function and $\small{L_n^{(\alpha,\beta)}}$ ($\small{{\gamma};x}$) is generalized Laguerre polynomials. Some integral formulas have been obtained. The Maple implementation has also been examined.
Keywords
infinite integrals;Laguerre polynomials;Hankel transform;
Language
English
Cited by
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