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2. Verify that the Legendre Polynomials Po, P1, P2, and P3 satisfy Legendre's equation (1 ~ x²) dy dx? dy dx 2x- + n(n + 1)у %— 0 - where M P,(x) = E(-1)" (2n – 2m)! 2" m! (п — т)!(п — 2т)!" m -2m т-0

2. Verify that the Legendre Polynomials Po, P1, P2, and P3 satisfy Legendre's equation (1 ~ x²) dy dx? dy dx 2x- + n(n + 1)у %— 0 - where M P,(x) = E(-1)" (2n – 2m)! 2" m! (п — т)!(п — 2т)!" m -2m т-0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. Verify that the Legendre Polynomials Po, P1, P2, and P3 satisfy Legendre's equation (1 ~ x²) dy dx? dy dx 2x- + n(n + 1)у %— 0 - where M P,(x) = E(-1)" (2n – 2m)! 2" m! (п — т)!(п — 2т)!" m -2m т-0
Transcribed Image Text:2. Verify that the Legendre Polynomials Po, P1, P2, and P3 satisfy Legendre's equation (1 ~ x²) dy dx? dy dx 2x- + n(n + 1)у %— 0 - where M P,(x) = E(-1)" (2n – 2m)! 2" m! (п — т)!(п — 2т)!" m -2m т-0
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