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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 -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
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)).
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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