Please help with the QM question below;

(a) The Rodrigues formula states that e Pe(ac) = dx (1) solves the Legendre equation d (1 - 202) dPe d.x dx + e(e+ 1) Pe(ac) = 0. (2) Prove this is indeed the case by showing that the Rodrigues formula reproduces the recursion relation derived in class for the coefficients ax in the Taylor expansion Pe(x) = Co akack. (b) Prove that the associate Legendre functions (m > 0) m Pm (a) = (1 - 22 )m/2 d dx Pe(ac) , (3) solve the differential equation found at non-trivial m and & in the angular part of the Schrodinger equation for spherically-symmetric potentials: dx dx (1 - 22) pm(x) + e(e+ 1) m 2 1 - 2 2 Pm (x) =0. ( 4)