The Chebyshev polynomials of the first kind can be otained from the recurrence relation, Tn+1(x) = 2xTn(x) − Tn−1(x) with T0(x) = 1 and T1(x) = x. a) Show that any two Chebyshev polynomials are orthogonal with respect to the weighting factor (1 − x)-1/2 in the closed interval [−1, 1]. b) Pick the first three Chebyshev polynomials and use Gram-Schmidt orthonormalization procedure to form an orthonormal set in the closed interval [−1, 1].

The Chebyshev polynomials of the first kind can be otained from the recurrence relation, Tn+1(x) = 2xTn(x) − Tn−1(x) with T0(x) = 1 and T1(x) = x. a) Show that any two Chebyshev polynomials are orthogonal with respect to the weighting factor (1 − x)-1/2 in the closed interval [−1, 1]. b) Pick the first three Chebyshev polynomials and use Gram-Schmidt orthonormalization procedure to form an orthonormal set in the closed interval [−1, 1].

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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