The formula of Rodrigues for the Legendre polynomial of degree n is given by dn Pn(x)...

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The formula of Rodrigues for the Legendre polynomial of degree n is given by dn Pn(x) = 12mm (x²-1)". n! 2n dxn Considering the analogous expressions for the Legendre polynomials Pn+1(x) and P₁-1(x) followed by their differentiation, show that Pn(x) = 2n+1 (Pn+1(x)-Pa-1(x)) for n=1,2,... The formula of Rodrigues for the Legendre polynomial of degree n is given by dn Pn(x) = 12mm (x²-1)". n! 2n dxn Considering the analogous expressions for the Legendre polynomials Pn+1(x) and P₁-1(x) followed by their differentiation, show that Pn(x) = 2n+1 (Pn+1(x)-Pa-1(x)) for n=1,2,...

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