I want to solve integral of following form $$\int_0^{\infty}x^{j}e^{-kx^{-l}\,_2F_1\left(m,n,o,-px^{-q}\right)-rx^2}dx$$ where $\,_2F_1$ is the gauss hypergeometric function, and all $j,k,l,m,n,o,p,q,r$ are positive values.
I have checked in Gradshteyn book but I have not found any formula which matches this form of equation. Please guide where can I find related information. If somebody can provide solution then I will be very thankful.
My Idea:
If we replace hypergeometric function by its series representation and further we use series representation for exponential function then maybe we can have some answer but the problem is how many terms we should consider in the series representation?