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Math Help - Double Fourier Series

  1. #1
    Junior Member
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    Cool Double Fourier Series

    Please help me : In calculus ,I only know Fourier Series,But in Real world,I need to know Double Fourier Series,and i don't know where to find the theory of double fourier series ,i use google,but don't find.
    so i want to know where can find this theory(basic),and which book discuss this good. can Someone would teach me this theory ?
    Thanks very much.....
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  2. #2
    MHF Contributor chisigma's Avatar
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    What does exact mean your expression 'double Fourier series?...

    a) a Fourier series in two dimesions

    b) a Fourier series in the complex domain

    c) something else

    Kind regards

    \chi \sigma
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  3. #3
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    I mean this:
    For Example:

    u_{L}(X,Y) = \frac{A_{00}}{2}+\sum_{n=1}^{\infty}{(A_{0n}cos(nX  ) + B_{0n}sin(nY))} + \sum_{m=1}^{\infty}{A_{m0}cos(mX) + B_{m0}sin(mY)}
    +\sum_{m=1}^{\infty}\sum_{n=\pm1}^{\pm\infty}{[A_{mn}cos(mX+nY) + B_{mn}sin(mX + nY)]}

    where

    A_{mn}+jB_{mn} = \frac{2}{(2\pi)^2}\int_{-\pi}^{\pi}\int_{-\pi}^{\pi}{u_{L}(X,Y)e^{j(mX+nY)}}dXdY
    thanks very much !
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