Question: Functional analysis If the sequence 1,x,x2, is orthogonalized in L2(1,1), the sequence en(x)=[21(2n+1)]1/2Pn(x) is obtained, where Pn(x)=2nn!1(dxd)n(x21)n. The functions Pn(x) are called Legendre polynomials

Functional analysis

Functional analysis If the sequence 1,x,x2, is orthogonalized in L2(1,1), the sequence

If the sequence 1,x,x2, is orthogonalized in L2(1,1), the sequence en(x)=[21(2n+1)]1/2Pn(x) is obtained, where Pn(x)=2nn!1(dxd)n(x21)n. The functions Pn(x) are called Legendre polynomials

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