# Thread: Double Fourier Series

1. ## 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.....

2. 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

$\displaystyle \chi$ $\displaystyle \sigma$

3. I mean this:
For Example:

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

where

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