How can I know that they are equivalent?
$$\sum_{n\in \mathbb Z} e^{-n^2\pi x} = \frac{1}{\sqrt{x}}\sum_{n\in \mathbb Z}e^{\frac{-n^2\pi}{x}} $$
I find this in wikipedia, in an article about the gamma function, where they used this property to find the analytic continuation of the zeta function. Thank you.
