A proof of the formula in (5.48) for the norm of the Legendre polynomial is based on
Question:
(a) First, prove that
by a repeated integration by parts.
(b) Second, prove that
by using the change of variables t = cos θ in the integral. The resulting trigonometric integral can be done by another repeated integration by parts.
(c) Finally, use the Rodrigues formula to complete the proof.
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