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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

    HallsofIvy

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    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
     
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