Series representation of the associated Legendre polynomial

Question

I have found the following identity for the associated Legendre polynomial to be true: $$ P_{n}^{m}(\tau)=\frac{n!(n+m)!}{2^n}\sum_{s=0}^{n-m}\frac{(-1)^{m+s}(1+\tau)^{n-m/2-s}(1-\tau)^{m/2+s}}{(n-s)!s!(m+s)!(n-m-s)!} $$ for individual values of integers $m$ and $n$ such that $0\leq m\leq n$. I can't seem to find a reference for this anywhere or see how to derive it from a known identity. If anyone could help me with either/both of these it would be much appreciated.