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