I need the solution for following integral and it has output in MATHEMATICA as:

`FullSimplify[ Integrate[x^(m - 1) Exp[-a x] Gamma[m, b/x], {x, 0, \[Infinity]}, Assumptions -> m > 1/2 && a > 0 && b > 0]] `

I really do not know the definition of the last Regularized Hypergeometric Function which has some numbers as superscripts.

Further, does anyone know how we can prove this analytically? Because there is very less integral formulas related to Regularized Hypergeometric Function.

Further, I found this output somehow numerically unstable for some large $ m$ .