A proof of the formula in (5.48) for the norm of the Legendre polynomial is based on

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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 Î¸ 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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Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

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Question Posted: Jun 17, 2016 08:51 AM

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A proof of the formula in (5.48) for the norm of the Legendre polynomial is based on

Question:

22k+1 (k!)2 (2k 1)!

Step by Step Answer:

a Integrating by parts k times and noting that the boundary terms are zero by ...View the full answer

Applied Linear Algebra

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