Numerical evaluation of Bessel function integrals for functions with exponential dependence

A numerical method for the calculation of Bessel function integrals is proposed for trial functions with exponential type behavior and evaluated for functions with and without explicit exponential dependence. This method utilizes the integral representation of the Bessel function to recast the problem as a double integral; one of which is calculated with Gauss-Chebyshev quadrature while the other uses a parameter-dependent Gauss-Laguerre quadrature in the complex plane. Accurate results can be obtained with relatively small orders of quadratures for the studied classes of functions.