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!

Fourier series for exponentials even or odd function?

  1. Aug 3, 2007 #1
    hi peeps. just a quick one.
    (a) how would you go around working out the fourier for exponential functions..
    simply something like e^x? (b) and how can this be applied to work out fourier series for cosh and sinh (considering cosh = e^x + e^-x / 2) etc etc..

    first of all.. is e^x even or odd function..
    i appreciate even function is: f(x) = f(-x)
    odd function is : -f(x) = f(-x)

    if for example , x =1.. e^x = e1...
    so f(x) = e1
    so e1 = 2.718...
    e(-1) = 0.367... which is neither f(x) or -f(x)?? so theres a sticky point as its not clear whether this is even or odd..??
  2. jcsd
  3. Aug 3, 2007 #2
    Not all functions are even, or odd. Some are neither, f(x)=ex is such a function.
  4. Aug 3, 2007 #3


    User Avatar
    Science Advisor

    ex is neither odd nor even. Given any function, f(x), we can define the even and odd parts of f by
    [tex]f_e(x)= \frac{f(x)+ f(-x)}{2}[/tex] and
    [tex]f_o(x)= \frac{f(x)- f(-x)}{2}[/tex]
    In particular, the even and odd parts of ex are
    [tex]\frac{e^x+ e^{-x}}{2}= cosh(x)[/tex] and
    [tex]\frac{e^x- e^{-x}}{2}= sinh(x)[/tex]
  5. Dec 9, 2011 #4
    okej but what about such function then
    [tex] f(x)=x^2e^{-x}[/tex] what kind of function do we get if we multiply an even function with a function that is neither odd nor even????
  6. Dec 9, 2011 #5
    ah I know
    it is neither odd nor even
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook