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/*z*^{n} 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 *z* – *z*_0. As an example, let’s look at the Laurent expansion of 1/Sin[*z*] at *z* == 2 Pi: