## A Mathematical Mystery

In my previous post on one-dimensional heat flow, I encountered sums of the form:

$$ \sum_{n=0}^\infty \frac{\pm 1}{2n+1} \exp \left( - (2n+1)^2 x \right) $$

A plot (involving the first 1000 terms) is shown below, and looks reasonable enough. Is this curve, which forms the limit of the series, a known function?