(20 pt)1) (8 pt)a) Consider the generating function for the Legendre polynomials. 1 g(x,t) = (1-2xt+t2)(1/2) = ∞ P(x) tn \t<1 n=0 Set 0 at both sides and by comparing the coefficients of powers of t at both sides show = that Podd (0) = 0, P2n (0)=(-1). (2n)! 22n (n!)2 (12 pt)b) Consider the function 0-1 <x<0 f(x) = 1 0<<1 Find the coefficients an in the series expansion of f(x) in a basis of Legendre polynomials Σα f(x)=anPn(x) 12=0