I came across the following function transformation: $$ \sum_{j=-\infty}^{\infty} e^{(-j^2\cdot t)} = \sqrt{\frac{\pi}{t}} \cdot \sum_{j=-\infty}^{\infty} e^{(-\frac{\pi^2}{t}\cdot j^2)} $$

where $ j \in \mathbb{Z}$ (i.e. integers).

Can anyone help me to understand why this relation is true? Thanks!