By manipulating the generating relation 1 -2xt+t = [ Pn (x)t, n=0 arrive at the...

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By manipulating the generating relation 1 √₁-2xt+t² = [ Pn (x)t", Σ n=0 arrive at the following recurrence relations involving the Legendre polynomials: (11a) (n+1) Pn+1(x) - (2n+1)xPn(x) +nPn-1(x) = 0 for n = 1,2,... (11b) xP(x)-P-1(x)-nPn(x) = 0 for n=1,2,... (11c) P+1(x)-P-1(x)-(2n+1)Pn(x) = 0 for n=1,2,... (11d) P+1(x)-xP(x) - (n+1)Pn(x) = 0 for n = 1,2,... By manipulating the generating relation 1 √₁-2xt+t² = [ Pn (x)t", Σ n=0 arrive at the following recurrence relations involving the Legendre polynomials: (11a) (n+1) Pn+1(x) - (2n+1)xPn(x) +nPn-1(x) = 0 for n = 1,2,... (11b) xP(x)-P-1(x)-nPn(x) = 0 for n=1,2,... (11c) P+1(x)-P-1(x)-(2n+1)Pn(x) = 0 for n=1,2,... (11d) P+1(x)-xP(x) - (n+1)Pn(x) = 0 for n = 1,2,...

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