Let Q0(x), Q1(x), . . . be an orthonormal sequence of polynomials; that is, it is an
Chapter 5, Problem 17(choose chapter or problem)
Let Q0(x), Q1(x), . . . be an orthonormal sequence of polynomials; that is, it is an orthogonal sequence of polynomials and _Qk_ = 1 for each k. (a) How can the recursion relation in Theorem 5.7.2 be simplified in the case of an orthonormal sequence of polynomials? (b) Let be a root of Qn. Show that must satisfy the matrix equation 1 1 1 2 2 . . . . . . . . . n2 n1 n1 n1 n Q0() Q1() ... Qn2() Qn1() = Q0() Q1() ... Qn2() Qn1() where the i s and j s are the coefficients from the recursion equations.
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