I want to evaluate the integration below;
$$ I_{n,j}= \int_{0}^{\infty} dx x^{2} e^{-\frac{x}{a}(\frac{1}{n}+\frac{1}{j})} L_{n-1}^{1} \left( \frac{2x}{na} \right)L_{j-1}^{1} \left( \frac{2x}{ja} \right) $$
$a$ is just constant and it is positive. $j$ and $n$ are positive integers. $L_p^q(x)$ is Laguerre polynomials and defined as
$$ L_p^q(x) = \frac{x^{-q}e^x}{p!} \frac{d^p}{dx^p} \left( x^{p+q}e^{-x}\right). $$
I can understand $I_{n,j}=I_{j,n}$. And how can we evaluate $I_{i,j}$ with general $i$ and $j$?