10. Let f be a continuous function with period 27. If f is an even function (that is, ƒ(x) = f(−x) for every x), and ∞ ao + Σ(an cos nt + b₂ sin nt) n=1 is the Fourier series for f, then bn = :0 for every n.
10. Let f be a continuous function with period 27. If f is an even function (that is, ƒ(x) = f(−x) for every x), and ∞ ao + Σ(an cos nt + b₂ sin nt) n=1 is the Fourier series for f, then bn = :0 for every n.
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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is the following statement true or false ?

Transcribed Image Text:10. Let f be a continuous function with period 27. If ƒ is an even function (that
is, f(x) = f(-x) for every x), and
∞
+ Σ(an cos nt + bn sin nt)
2
n=1
ao
is the Fourier series for f, then bn
=
0 for every n.
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