I need to solve the following integral $$\int_{a}^{\infty}\Gamma\left(b,\frac{d}{x}\right)x^{k-1}e^{-cx}dx$$ where $a>0$, $b>0$ and $c>0$. I checked in wolfram alpha but it does not provide any answer. Further, I checked the book of Gradeshteyn (Eq. 6.456) but it can be seen that there are slight differences in my problem Eq. 6.456. Thanks in advance.
My Attempt:
In my attempt I put $b=1$ and the answer is of following form $$\int_a^{\infty}e^{-\frac{d}{x}-x}x^{k-1}dx$$ and again Eq. 3.471.9 of Gradeshteyn book is almost similar to the above equation with one exception that lower limit is $0$. How to solve for a general positive limit? Thanks in advance.