Question: 3) The Chebyshev polynomials of the first kind can be otained from the recurrence relation, Tn+1(2) = 2rT(1) - Tn-1(r) with To(x) = 1

3) The Chebyshev polynomials of the first kind can be otained from

3) The Chebyshev polynomials of the first kind can be otained from the recurrence relation, Tn+1(2) = 2rT(1) - Tn-1(r) with To(x) = 1 and T(x) = 2. a) Show that any two Chebyshev polynomials are orthogonal with respect to the weighting factor (1-2)- in the closed interval [-1, 1]. [4] b) Pick the first three Chebyshev polynomials and use Gram-Schmidt orthonormalization procedure to form an orthonormal set in the closed interval [-1,1]. [6]

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