Find the trigonometric Fourier series for the function f(x): [-T/2, T/2] - R given by the expression: f(x) = ² FS(2)=sinhr|1+2 +[₁ FS(x) = FS(x) = FS(x) sinh r sin T 70 sinh T T [ 21 12 2 ∞ (-1)" n² +1 + Σn=1 + ΣΩ + Ex-1 (-1)" n²+1 (-1)" n+1 (cos 2nx + n sin 2nx) 2na)]. (-1)" n²+1 (cos 2nx - n sin 2nx) nx)]. (cos 2nx - (cos 2nx - n sin 2nx) sin 2nx)

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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Find the trigonometric Fourier series for the function f(x): [-π/2, π/2] → R given by the
expression:
f(x) = ²²²
e²x
2
O
O
FS(x)=sinhr|1+En
FS (x) =
FS(x) =
O
FS(x)
=
sinh a
IT
sin πT
π
sinh a
7
2
2
(-1)"
+Σn-1 n²+1
+ Σn-1
11
2
(-1)"
n² +1
+ ΣΑ 1
(-1)"
n+1
(-1)"
n=1 n²+1
(cos 2nx + n sin 2nx)
1.
(cos 2nx n sin 2nx)
nx)].
(cos 2nx
-
-
(cos 2nx
L
n sin 2nx)
sin 2na)].
Transcribed Image Text:Find the trigonometric Fourier series for the function f(x): [-π/2, π/2] → R given by the expression: f(x) = ²²² e²x 2 O O FS(x)=sinhr|1+En FS (x) = FS(x) = O FS(x) = sinh a IT sin πT π sinh a 7 2 2 (-1)" +Σn-1 n²+1 + Σn-1 11 2 (-1)" n² +1 + ΣΑ 1 (-1)" n+1 (-1)" n=1 n²+1 (cos 2nx + n sin 2nx) 1. (cos 2nx n sin 2nx) nx)]. (cos 2nx - - (cos 2nx L n sin 2nx) sin 2na)].
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