Wednesday, September 26, 2012

Laurent Series as Fourier Expansion

During our math methods lecture yesterday, this pair of formulas came up:

Which was very cool because it has the feel of a Fourier series.  It's a sum that approximates a function... The coefficients are line integrals over the contour as opposed to integrals over the conjugate variable.  This is the last in a string of similarities between complex analysis and Fourier analysis that have been building in class lately.  So, it was very cool to find a set of class notes from Dr. Jeffrey Rauch of UMich that directly addresses this:

http://www.math.lsa.umich.edu/~rauch/555/laurentfourier.pdf

Thanks Dr. Rauch!

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