I am a computer scientist revisiting integration after a long time. I am stuck with this simple-looking integral that's turning out to be quite painful (to me). I was wondering if one of you could help.
The goal is to solve the integral
Note that this is the convolution of the Gaussian centered around 0 with the function that equals $x^n$ for $x > 0$, and 0 elsewhere (modulo scaling).
In particular, I would be interested in seeing any relationship with the integral
which I have worked out.
Thanks in advance,