Recall the definition of associated Legendre function in the book by Eq. (8.53) mam Pm (x) = (-1)m(1 - x2 )2 (1 - x2)2 dl+m dx m Pi(x) = (-1)m 2'!! dxl+m (x2 - 1)' Show that, for I + m even, Pm(0) = (-1)(1+m)/2 (1 + m - 1)! (1 - m)! (Hint: Identify the term that is non-zero and use the Leibniz rule of differentiation.)P"() = (-1)"(1- u2)m/2 P(u) dum