(Solution) - A proof of the formula in 5 48 for the norm -(2025 Original AI-Free Solution)

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Academic Level: Undergrad. (yrs 3-4)

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A proof of the formula in (5.48) for the norm of the Legendre polynomial is based on the following steps.
(a) First, prove that

by a repeated integration by parts.
(b) Second, prove that

by using the change of variables t = cos ? 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.