TAG: Complex Analysis
February 25, 2011– 1

Why did the mathematician name his dog Cauchy? Because he left a residue at every pole!

But could the mathematician find the poles and their residues for a given function? He certainly could, with the help of Wolfram|Alpha.

We are proud to announce that Wolfram|Alpha has added residues and poles to its ever-expanding library of mathematical data that it can compute! To showcase this behavior, let’s first recall just what a pole is.

In the study of complex analysis, a pole is a singularity of a function where the function behaves like 1/zn at z == 0 .

More technically, a point z_0 is a pole of a function if the Laurent series expansion of the function about the point z_0 has only finitely many terms with a negative degree of zz_0. As an example, let’s look at the Laurent expansion of 1/Sin[z] at z == 2 Pi:

Laurent expansion More »