# Function transformation of exponentials

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!

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