I am trying to evaluate the following integral involving the Gauss Hypergeometric function, power, exponential and a Bessel Function:
$$ \int_0^\infty x e^{-cx^2} {_2F_1(1,\frac{2} {ab},1+\frac{2} {ab},-zx^{-a})I_2(qx)dx} $$ where $a,b,c,z,q > 0 $ real numbers. Can you please provide some hints on solving this integral?
Thank you for your time and patience