Communications of the
Korean Mathematical Society CKMS

The principal aim of the paper is to investigate new integral expression $$\int_0^\infty {x^{s+1}e^{-\sigma x^2}L_m^{\left( {\gamma ,\delta } \right)} \left( {\zeta ;\sigma x^2} \right)L_n^{\left( {\alpha ,\beta } \right)} \left( {\xi ;\sigma x^2} \right)J_s \left( {xy} \right)dx}, $$ where $y$ is a positive real number; $\sigma $, $\zeta \;$ and $\xi_{ }$ are complex numbers with positive real parts; $s,\alpha ,\beta ,\gamma $ and $\delta $ are complex numbers whose real parts are greater than $-1$; $J_n \left( x \right)$ is Bessel function and $L_n^{\left( {\alpha ,\beta }\right)} \left( {\gamma ;x} \right)_{ }$ is generalized Laguerre polynomials. Some integral formulas have been obtained. The Maple implementation has also been examined.

Keywords: infinite integrals, Laguerre polynomials, Hankel transform

MSC numbers: 65A05, 33C45, 44A15