Use the generating function to find the first five (5) Legendre polynomials and verify their your...

Use the generating function to find the first five (5) Legendre polynomials and verify their your answer using Rodrigues's formula.

Expert Solution

On equating thevcoefficients of tⁿ for n= 0, 1, 2, 3, 4 we find first few Legendre polynomial

By Rodrigues's formula

P₀(x) = 1

p₁(x) = (1/1! × 2¹) (d/dx)(x² - 1) = (1/2)(2x) = x

Similerly putting n = 4 we find P₄(x) = (1/8)(35x⁴ - 30 x² + 3)

Colby Messinger answered 7 months ago

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