12.14 Show that the Fourier series for the function y(x) = |x| in the range - < x < T is T TIR y(x) By integrating this equation term by term from 0 to x, find the function g(x) whose Fourier series is ∞ ∞0 m=0 4 cos(2m +1)x Σ π (2m + 1)² m=0 sin(2m +1)x (2m + 1)³
12.14 Show that the Fourier series for the function y(x) = |x| in the range - < x < T is T TIR y(x) By integrating this equation term by term from 0 to x, find the function g(x) whose Fourier series is ∞ ∞0 m=0 4 cos(2m +1)x Σ π (2m + 1)² m=0 sin(2m +1)x (2m + 1)³
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
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![Deduce the value of the sum S of the series
1 1
+
33 53
1
1
73
+](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F775c65b2-d298-4974-84c2-1b9ec352df93%2F30d7989e-6207-4f53-aec8-77816842f1a8%2Fjxru41l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Deduce the value of the sum S of the series
1 1
+
33 53
1
1
73
+
![12.14
Show that the Fourier series for the function y(x) = |x| in the range −ñ ≤ x < π
is
π
2
4
y(x) S
m=0
By integrating this equation term by term from 0 to x, find the function g(x)
whose Fourier series is
+|R
4
π
m=0
cos(2m +1)x
(2m + 1)²
π
sin(2m + 1)x
(2m + 1)³](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F775c65b2-d298-4974-84c2-1b9ec352df93%2F30d7989e-6207-4f53-aec8-77816842f1a8%2Frtlvot8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:12.14
Show that the Fourier series for the function y(x) = |x| in the range −ñ ≤ x < π
is
π
2
4
y(x) S
m=0
By integrating this equation term by term from 0 to x, find the function g(x)
whose Fourier series is
+|R
4
π
m=0
cos(2m +1)x
(2m + 1)²
π
sin(2m + 1)x
(2m + 1)³
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