I'm working in asymptotic expansions and it appear this integral
$$\int_0^{\infty}e^{-t^{2m}}t^n(t-a)^{s}dt,\quad a\in\mathbb{R}$$
where $m,n\in\mathbb{N}$ and $s\in(-1,0]$.
When $a=0$, it becomes a Gamma function. I wonder if it can be written in terms of some special function when $a\neq0$.
Any help will be welcomed.