{che (x) = sin [(k+1)x]. k = 0, 1, 2, 3, ... .:}₁ on 11. Consider the family of functions x € [-T, π]. (a) Show that this family is orthogonal with respect to the inner product π (f,g) = ™* f(a)g(x) dx. (b) Give the formula for Fourier coefficients for a function f(x) with respect to this family, f(x) ~ S(x) = ΣCkøk(x). k=0
{che (x) = sin [(k+1)x]. k = 0, 1, 2, 3, ... .:}₁ on 11. Consider the family of functions x € [-T, π]. (a) Show that this family is orthogonal with respect to the inner product π (f,g) = ™* f(a)g(x) dx. (b) Give the formula for Fourier coefficients for a function f(x) with respect to this family, f(x) ~ S(x) = ΣCkøk(x). k=0
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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Please show a step-by-step solution. Do not skip steps, and explain your steps. Write it on paper, preferably. Make sure the work is clear.
![{che (x) = sin [(k+1)x]. k = 0, 1, 2, 3, ... .:}₁
on
11. Consider the family of functions
x € [-T, π].
(a) Show that this family is orthogonal with respect to the inner product
π
(f,g) = ™* f(a)g(x) dx.
(b) Give the formula for Fourier coefficients for a function f(x) with respect to this
family,
f(x) ~ S(x) = ΣCkøk(x).
k=0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3cb378ba-be87-4838-bd31-84fa6b2aaf1f%2F0f2f357e-3b7d-4fb6-a32f-e9bceeed4ba4%2Frcwcbsr_processed.png&w=3840&q=75)
Transcribed Image Text:{che (x) = sin [(k+1)x]. k = 0, 1, 2, 3, ... .:}₁
on
11. Consider the family of functions
x € [-T, π].
(a) Show that this family is orthogonal with respect to the inner product
π
(f,g) = ™* f(a)g(x) dx.
(b) Give the formula for Fourier coefficients for a function f(x) with respect to this
family,
f(x) ~ S(x) = ΣCkøk(x).
k=0
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