Introduction to Electrodynamics · Problem 3.17

Potentials — David J. Griffiths

Physics · legendre-polynomials

Problem

Derive

P_3(x)

from the Rodrigues formula, and check that

P_3(\cos\theta)

satisfies the angular equation (3.60) for

l = 3

. Check that

P_3

and

P_1

are orthogonal by explicit integration.