TITLE: complex fourier coefficients, introduced by?
QUESTION [16 upvotes]: I remember reading somewhere that the complex Fourier coefficients were introduced by an engineer sometime around 1900, but I can't find anymore this information.
Does anyone know the name of this person and where I can find a reference to it?
EDIT: I state the question more clearly: "Who was it that first wrote a Fourier series not as a sum of sines and cosines but as a sums of complex exponentials, with the relative formula for the coefficients?". I may be totally wrong about this all, since I don't remember well and that's why I'm asking. Also don't take the 1900 thing seriously, I may be off by 50+ years.

REPLY [3 votes]: As another data point, my copy of Whitaker and Watson  A course of Modern Analysis, 4th edition from 1927 uses the trig versions for basically everything, but Example 1, $$f(z) = \sin(z) - 1/2 \sin 2z + 1/3 \sin(3x) -\ldots$$ is immediately converted to $$f(z) = \frac{1}{2}i(e^{iz}-1/2e^{2iz}+\ldots)+\frac{1}{2}i(e^{-iz}-1/2e^{2iz}+\ldots)$$ The references given "for a fuller account of investigations subsequent to Riemann" are Hobson's Functions of a Real Variable and de la Vallée Poussin's Cours d'Analyse Infinitésimale.