I already prove other properties of the Legendre polynomials, like: P_n(-x) = (-1)^nP_n(x) P_{2n+1}(0) = 0 P_n(\pm1)= (\pm1)^n But I can't get this: P_{2n}(0) = \frac{(-1)^n(2n-1)!}{2^{2n-1}((n-1)!)^2} I'm so glad if someone can help me with...