(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Expand the function in to Fourier series

[tex] f(x) = coshx, |x|\leq \pi[/tex]

2. Relevant equations

Fourier series will be

[tex] C_{n}=\frac{1}{2\pi}\int_{-\pi}^{\pi}(\frac{e^{x}+e^{-x}}{2}})e^{-inx}}dx[/tex]

[tex] \frac{1}{4\pi}\int_{-\pi}^{\pi}({e^{x}e^{-inx})dx+ \frac{1}{4\pi}\int_{-\pi}^{\pi}(e^{-x}e^{-inx})dx[/tex]

3. The attempt at a solution

I calculate both integrals separately

[tex] \frac{1}{4\pi}\int_{-\pi}^{\pi}({e^{x}e^{-inx})dx=\frac{1}{4\pi}\int_{-\pi}^{\pi}({e^{x-inx})dx=\frac{1}{4\pi}\frac{e^{x-inx}}{1-in}[/tex]

I substitute [tex] x=\pm\pi \Rightarrow \frac{(-1)^n}{1-in}[e^{\pi}-e^{-\pi}][/tex]

1. The problem statement, all variables and given/known data

and the other one gives me

[tex]\frac{(-1)^n}{-1-in}[e^{-\pi}-e^{\pi}][/tex]

is this correct so far?

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# Homework Help: Fourier series

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