2. Using the Generating Function G(x, t) for the Legendre Polynomials (1 -2xt + 12 ) - 1/2 - > Pn (x) t" Prove the following identities: +1 [P, (x) dx = 2 (a) -1 2n +1 (b) P,, (-1) = (-1)" ( c) nP_ (x) +(n+1)Pn+ (x) -(2n+1)xP, (x) =0