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My teacher wrote the following about the legendre function without proof

1) $P^{-m}_{n}(x)=(-1)^{m}\frac{(n-m)!}{(n+m)!}P_{n}^{m}(x)$

2) $P_{2n}(0)=\frac{(-1)^{m}}{\sqrt{\pi}}\frac{\Gamma(n+\frac{1}{2})}{\Gamma(n+1)}$

I search for proof online but couldn't find any. Does anyone know how to proof these properties?

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