I asked the question Fourier series is to Fourier transform what Laurent series is to …? over at MSE, since that's where my questions usually belong to. But since I couldn't find any resources on it, I was wondering if it were actually adequate for migration to MO?
To summarize that question, it is about the similarity between Fourier analysis and the Laurent series on a circle and whether the $r\to\infty$-limit of the latter a) makes sense b) also yields an integration similar to the Fourier series turning into the Fourier transform and c) whether its useful.