Mathematically, these are three distinct, although related beasts.
Laplace transform (function f(x) defined from 0 to inf) integral of
f(x)e-xt, defined for t=0.
Fourier transform (function f(x) defined from -inf to inf) integral of
f(x)e-itx defined for all real t.
Complex Fourier series (function f(x) defined on finite interval -
simplify by making it (0,1)) Coeficients (cn) are given by
integral of f(x)e-2(pi)inx, where n ranges over all
integers. The series terms are cne2(pi)nx
Real Fourier series use sin and cos instead of exp function.

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