Chapter 5, PROBLEM SET 5.2 #15

Associated Legendre functions P^{k}_{n}(x)_{?}are needed, e.g., in quantum physics. They are defined by

and are solutions of the ODE

where q(x) = n(n + 1) - k^{2}/(1 - x^{2}). Find P^{1}_{1}(x), P^{1}_{2}(x), P^{2}_{2}(x), and P^{2}_{4}(x) and verify that they satisfy (16).

PROBLEM SET 5.2:

PROBLEM SET 5.3:

PROBLEM SET 5.4:

PROBLEM SET 5.5: