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)
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
Related questions
Question
![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)].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fe9d10e-89b5-480b-b9fb-b8733688f212%2Fa1624b7b-55ad-4f5b-974c-5d3fb82c35a2%2Fpveaue_processed.jpeg&w=3840&q=75)
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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