The Laurent series is a power series with the form:
Laurent series = 1 + z + z2 + z3 + z4 + ...
Where each term is defined as:
an = bn / n2
For a given function f(z) that is analytic at 0, the Laurent series is given by:
L(z) = 1 + f''(0)z + ...
Why is this series so cool?
This series is a way to express an analytic function as a power series. It's like a secret handshake between math and computer science, but without the awkward small talk.
But, in all seriousness, the Laurent series is an important tool for analyzing functions that don't have a simple power series expansion, like rational or trigonometric functions.