1. Tchebycheff polynomials of the second kind. These are defined on [-1,1] by Un(x)sin (n + 1)0/sin 0 where x = cos 8. Show that these functions are polynomials and areorthogonal with respect to the inner productorthonormal set? Ans. {/2/ Un}.| f(x)g(x) Vĩ – x² dx. What is the

We are given Un(x)=sin (n+1)θsin θ where x=cos θ and which are defined on [-1, 1]. First, we will…

Answered: Tchebycheff polynomials of the second…

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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Tchebycheff polynomials of the second kind. These are defined on [-1,1] by U„(x) sin (n + 1)0/sin 6 where x = c cos 8. Show that these functions are polynomials and are orthogonal with respect to the inner product f(x)g(x) Vĩ – x² dx. What is the orthonormal set? Ans. {V2/ Un}. -