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

Chapter 5, PROBLEM SET 5.2 #15

Associated Legendre functions Pkn(x)?are needed, e.g., in quantum physics. They are defined by

image

and are solutions of the ODE

image

where q(x) = n(n + 1) - k2/(1 - x2). Find P11(x), P12(x), P22(x), and P24(x) and verify that they satisfy (16).

Related Book For answer-question

Advanced Engineering Mathematics

10th edition

Authors: Erwin Kreyszig

ISBN: 978-0470458365