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
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Question
100%
Deduce the value of the sum S of the series
1 1
+
33 53
1
1
73
+
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
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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