In particular, they studied the following value of Δ:
Δ=41010(∑n=−∞n=+∞exp⁡−n21010)2.\Delta =\frac{4}{10^{10}}\left ( \sum_{n=-\infty}^{n=+\infty}\exp \frac{-n^2}{10^{10}} \right )^2.
The series appearing in this value converges very slowly… With a million terms (that is, with the index ranging from −500,000 to 500,000), we obtain 3.14159265358013… for Δ, an approximation of π to eleven significant digits! So, despite the extremely slow convergence, we might expect Δ to be equal to π.
Well, it is not! The number Δ is not equal to π. Far more surprisingly, it shares more than forty-two billion decimal digits with π! That is an enormous number: writing them out would take more than twelve million pages. Beyond that, however, the digits differ—which is only natural, one might say, since the two values are not equal!