How can I represent $$(t^2+1)^{-1/2}$$ as a power series? What I know is $$\frac1{1-t} = \sum_{n=0}^\infty t^n$$ $$-1<t<1$$
Additional: I encountered this problem when solving Legendre polynomial relation
$$P_{2n}(0)=(-1)^n\frac{1\cdot3\cdots(2n-1)}{2\cdot 4\cdots (2n)}$$ using the generating function.