If we are able to rewrite our integral of Eq. (7) with a weight function \( W(x)=x^{\alpha}e^{-x} \) with integration limits \( [0,\infty) \), we could then use the Laguerre polynomials. The polynomials form then the basis for the Gauss-Laguerre method which can be applied to integrals of the form $$ \begin{equation*} I=\int_0^{\infty}f(x)dx =\int_0^{\infty}x^{\alpha}e^{-x}g(x)dx. \end{equation*} $$