In this video, a mathematics guy explains how a two-dimensional grid can represent a list of every algebraic number exactly once. Then, he explains how Cantor diagonalisation to construct a real number outside the set of algebraic numbers. The number in question is:
0.1001111100111111111001111111111111001111111111111111100111111111111111111111...
This number can be expressed as (correct me if I'm wrong) $\displaystyle\frac{1}{9}-11\sum_{n\in\mathbb{Z}^{+}}\left(10^{-2n^2-n}\right)$.
My question is this: The strings of ones increase in length linearly, and numbers such as 0.1101001000100001000001000000100000001000000001... can be expressed in terms of Jacobi Theta functions. Is it possible to express the infinite sum in terms of Theta functions?