- #1
stunner5000pt
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Find the FOurier Series in terms of [itex] \phi_{n} = \sin(nx) [/itex] of the step function
f(x) = 0 for [itex] 0 \leq x \leq \frac{1}{2} \pi [/tex]
f(x) =1 for [itex] \frac{1}{2} \pi < x \leq \pi [/itex]
now i have no problem finding the series for each branch. But how would i combine them?
for the 0 to 1/2 pi
[tex] \frac{4}{\pi} \sum_{n=1}^{\infty} \sin nx [/tex]
for the 1/2 pi to pi
[tex] \frac{-4}{\pi} \sum_{n=1}^{\infty} \frac{1}{n} \left((-1)^n + \cos(\frac{n \pi}{2}) \right) [/tex]
please help me on combining the two!
Thank you for your help
f(x) = 0 for [itex] 0 \leq x \leq \frac{1}{2} \pi [/tex]
f(x) =1 for [itex] \frac{1}{2} \pi < x \leq \pi [/itex]
now i have no problem finding the series for each branch. But how would i combine them?
for the 0 to 1/2 pi
[tex] \frac{4}{\pi} \sum_{n=1}^{\infty} \sin nx [/tex]
for the 1/2 pi to pi
[tex] \frac{-4}{\pi} \sum_{n=1}^{\infty} \frac{1}{n} \left((-1)^n + \cos(\frac{n \pi}{2}) \right) [/tex]
please help me on combining the two!
Thank you for your help