1. (Chebyshev) This problem is a continuation of the example from class involving the Chebyshev polynomials....

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1. (Chebyshev) This problem is a continuation of the example from class involving the Chebyshev polynomials. These Chebyshev polynomials, T. (r) are easily generated by the recursion relationship: To (r) = 1 T₁(x) = x Tn+1(x) = 2xTn(x) - Tn-1(x) n = 2, 3,... (1) (a) Write out the first six Chebyshev polynomials (To, T₁,...,T5) using the recursion relationship (1). (b) Apply the Gram-Schmidt orthogonalization procedure to represent the basis set {To(x), T₁(x), T₂(x), T3(x), T₁(x), T5(x)} as an orthogonal set. Let the inner product be defined as we did in class with the interval from a = -1 to b = 1. That is, (51, 52) = (T,T;) = | T;(2)T; (x) dx (2) 1. (Chebyshev) This problem is a continuation of the example from class involving the Chebyshev polynomials. These Chebyshev polynomials, T. (r) are easily generated by the recursion relationship: To (r) = 1 T₁(x) = x Tn+1(x) = 2xTn(x) - Tn-1(x) n = 2, 3,... (1) (a) Write out the first six Chebyshev polynomials (To, T₁,...,T5) using the recursion relationship (1). (b) Apply the Gram-Schmidt orthogonalization procedure to represent the basis set {To(x), T₁(x), T₂(x), T3(x), T₁(x), T5(x)} as an orthogonal set. Let the inner product be defined as we did in class with the interval from a = -1 to b = 1. That is, (51, 52) = (T,T;) = | T;(2)T; (x) dx (2)

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The problem asks you to write out the first six Chebyshev polynomials using the recursion relationship given in the imageand then apply the GramSchmidt orthogonalization procedure to represent the bas... View the full answer