17. In this question, we will expand the Dirac delta-function centered at the origin in terms of Legendre Polynomials, i.e. we will find the az in the expression 8(x) = P(x) 1=0 (a) Use the orthogonality relationship of the Legendre polynomials to find the a in terms of P(0) (b) We now need to find the P(0). Use the generating function ∞ 1 (x,h)= = √1-2xh+h2 Σh' Pi(z) 1=0 to show that for odd I, we have P2n-1(0) = 0 and that for even I we have (2n)! P2m (0)=(-1) 22n (n!)² for n = 0, 1, 2,...