Hi,
We know that the Gaussian integral is
\int_{-\infty}^{+\infty}e^{-\frac{x^2}{a^2}}dx=a\sqrt{\pi}
However, if the gaussian function is discrete in x, what is the result of
\sum_{n=0}^{+\infty}e^{-\frac{n^2}{a}} = \\?
where n is natural number, that is n=0,1,2,3....