Complex Form of the Fourier Series We had seen in class that the complex form of a Fourier Series is given by pa+P Ar) = E " Ax)e2inzxi/P dx Ax) = c,e-2inrx/P with Cne' Cn P n- for any constant a. Determine the coefficients c, for the function Ax) = |sin(x)|.
Complex Form of the Fourier Series We had seen in class that the complex form of a Fourier Series is given by pa+P Ar) = E " Ax)e2inzxi/P dx Ax) = c,e-2inrx/P with Cne' Cn P n- for any constant a. Determine the coefficients c, for the function Ax) = |sin(x)|.
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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![**Complex Form of the Fourier Series**
We had seen in class that the complex form of a Fourier Series is given by
\[
f(x) = \sum_{n=-\infty}^{+\infty} c_n e^{-2\pi inx/P}
\]
with
\[
c_n = \frac{1}{P} \int_{a}^{a+P} f(x) e^{2\pi inx/P} \, dx
\]
for any constant \( a \). Determine the coefficients \( c_n \) for the function
\[
f(x) = |\sin(x)|.
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Transcribed Image Text:**Complex Form of the Fourier Series**
We had seen in class that the complex form of a Fourier Series is given by
\[
f(x) = \sum_{n=-\infty}^{+\infty} c_n e^{-2\pi inx/P}
\]
with
\[
c_n = \frac{1}{P} \int_{a}^{a+P} f(x) e^{2\pi inx/P} \, dx
\]
for any constant \( a \). Determine the coefficients \( c_n \) for the function
\[
f(x) = |\sin(x)|.
\]
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