Question: Ty(x) = 4p- 1r. U. = 1. U,(r) = 2r, U,(x) = 47- 1. U,(x) = &] - 4r. Show that the Chebyshev polynomials T,,(x)

Ty(x) = 4p- 1r. U. = 1. U,(r) = 2r, U,(x) = 47- 1. U,(x) = &] - 4r. Show that the Chebyshev polynomials T,,(x) are orthogonal on the interval -1 5 x # I with respect to the weight function r(x) (Hint. To evaluate the integral, set arccos x = 6.) Verify that T(x). n = 0. 1. 2. 3. satisfy the Chebyshev equation (1 My = 0

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