- Thread starter
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- #1
- Jan 26, 2012
- 995
Thanks to those who participated in last week's POTW!! Here's this week's problem!
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Problem: Let $f(x)=\exp(-|x|)$ for $-\pi\leq x\leq \pi$ be a $2\pi$-periodic function.
Show that it's Fourier series is $\displaystyle\frac{e^{\pi}-1}{\pi e^{\pi}}+\frac{2}{\pi e^{\pi}}\sum_{n=1}^{\infty} \frac{1}{n^2+1}(e^{\pi}-(-1)^n) \cos(nx)$.
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Remember to read the POTW submission guidelines to find out how to submit your answers!
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Problem: Let $f(x)=\exp(-|x|)$ for $-\pi\leq x\leq \pi$ be a $2\pi$-periodic function.
Show that it's Fourier series is $\displaystyle\frac{e^{\pi}-1}{\pi e^{\pi}}+\frac{2}{\pi e^{\pi}}\sum_{n=1}^{\infty} \frac{1}{n^2+1}(e^{\pi}-(-1)^n) \cos(nx)$.
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Remember to read the POTW submission guidelines to find out how to submit your answers!