Find the FOurier Series in terms of [itex] \phi_{n} = \sin(nx) [/itex] of the step function(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Fourier Series

**Physics Forums | Science Articles, Homework Help, Discussion**