How to reconcile inverse Laplace transform?

29 Views Asked by At

I want to know which Laplace transform will give me $t^n$. If I use the inverse Laplace Transform on $t^n$, I get $s^{-n-1}/\Gamma(-n)$, but the gamma function is undefined for negative values. It's obviously well defined for non-integer values, so is there some way to get this formula to work for values arbitrarily close to negative integers?