1 dn If the Legendre polynomials Pn(x) = 2n! dxn (x - 1) form a complete...

 

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1 dn If the Legendre polynomials Pn(x) = 2"n! dxn (x - 1)" form a complete set of eigenfunctions with a weight function w(x)=1, and their orthogonality relation is given by the equation LPm -1 Pm(x)Pn(x) dx = 2/(2n+1) 8nm a. Find Po(x), P2(x), P3(x) and P4(x) b. Expand the step function f(x) = {1 -1 1 dn If the Legendre polynomials Pn(x) = 2"n! dxn (x - 1)" form a complete set of eigenfunctions with a weight function w(x)=1, and their orthogonality relation is given by the equation LPm -1 Pm(x)Pn(x) dx = 2/(2n+1) 8nm a. Find Po(x), P2(x), P3(x) and P4(x) b. Expand the step function f(x) = {1 -1