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1 60 The Legendre polynomials In are defined for n MEN by 1 Py : IR - IR , Put*1:= d 2 and have many

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1 60 The Legendre polynomials In are defined for n MEN by 1 Py : IR - IR , Put*1:= d 2 and have many applications in mathematics and physics . show it: a ) In is a polynomial of degrees and has exactly real zeros in the interval ( 1,1 ) b Pu satisfies Legendre's differential equation (1 -22) Pl(x) - 2x Ph(x) +n(n + 1) Pn(x) =0, rER

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