Problem 3 Please prove Thm. 5.6 Differentiation of Fourier Series Let f be continuous on -L, L) and suppose f(L) = f(-L). Let f' be piecewise continuous on [-L, L]. Then f(r) equals its Fourier series for -LS&SL 1 an and, at each point in (-L, L) where f"(a) exists, nx na f'(x)=(-a, sin("") + b, cos("")) L n=1
Problem 3 Please prove Thm. 5.6 Differentiation of Fourier Series Let f be continuous on -L, L) and suppose f(L) = f(-L). Let f' be piecewise continuous on [-L, L]. Then f(r) equals its Fourier series for -LS&SL 1 an and, at each point in (-L, L) where f"(a) exists, nx na f'(x)=(-a, sin("") + b, cos("")) L n=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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![Problem 3
Please prove Thm. 5.6 Differentiation of Fourier Series Let f be continuous on -L, L] and
suppose f(L) = f(-L). Let f' be piecewise continuous on [-L, L]. Then f(r) equals its Fourier series for
-L≤x≤L,
f(x)= ao+a, cos(") +- b, sin(
L
and, at each point in (-L, L) where f"(a) exists,
f'(x) = (
-Σ(-a, sin (¹) + b₂ cos(
ᏤᏤᏤᎳᏗ .
(HTF)).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faa452579-39b1-4d40-9301-36b64e7204f2%2F69c5bb44-7abc-4117-9bc7-ecbafb5d409f%2Fq6ud1jv_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 3
Please prove Thm. 5.6 Differentiation of Fourier Series Let f be continuous on -L, L] and
suppose f(L) = f(-L). Let f' be piecewise continuous on [-L, L]. Then f(r) equals its Fourier series for
-L≤x≤L,
f(x)= ao+a, cos(") +- b, sin(
L
and, at each point in (-L, L) where f"(a) exists,
f'(x) = (
-Σ(-a, sin (¹) + b₂ cos(
ᏤᏤᏤᎳᏗ .
(HTF)).
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