1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Fourier series convergence

  1. Jun 15, 2012 #1
    1. The problem statement, all variables and given/known data


    This series is what dictates the graph above.


    3. The attempt at a solution

    I don't understand what's going on. If they're using the series that i pasted below then why aren't they multiply each value in the brackets by -2/pi?

    I also don't get why terms in the brackets are

    [(-2pi + 0) + f(-2pi - 0)]

    Where did they come from? Where does 1/2 come from that multiplies the brackets. very confused.
  2. jcsd
  3. Jun 15, 2012 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    They could have. The ##\frac {-2}\pi## was just factored out.
    Your function isn't defined at the jumps, like at ##-2\pi##. To get the average value at the jumps you need the average of the right and left limits:$$
    \lim_{h\rightarrow 0+}\frac{f(-2\pi + h)+f(-2\pi -h)}{2}$$Those limits give the value of the function at ##-2\pi\ ##"coming from" the left and right. The expression ##f(-2\pi + 0)+ f(-2\pi -0)##is just a shorthand notation for the limits, and you add them and divide by 2 to get the average.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook