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(a) Find the Fourier series for the periodic function defined by f(x) ex, –n s x < T. Hint: Recall that sinh x = (e* – e-*)/2.

(a) Find the Fourier series for the periodic function defined by f(x) ex, –n s x < T. Hint: Recall that sinh x = (e* – e-*)/2.

Advanced Engineering Mathematics
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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5. (a) Find the Fourier series for the periodic function defined by f(x) = ex, -n s x < T. Hint: Recall that sinh x = (ex – e-x)/2. (b) Sketch the graph of the sum of this series on the interval -5n s x < 5x. (c) Use the series in (a) to establish the sums 1 1 n² +1 -1 2 tanh n and (-1)" 1 1 2 sinh n² +1
Transcribed Image Text:5. (a) Find the Fourier series for the periodic function defined by f(x) = ex, -n s x < T. Hint: Recall that sinh x = (ex – e-x)/2. (b) Sketch the graph of the sum of this series on the interval -5n s x < 5x. (c) Use the series in (a) to establish the sums 1 1 n² +1 -1 2 tanh n and (-1)" 1 1 2 sinh n² +1
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