New proof of the Gaussian integral using the residue theorem with links to the Riemann Zeta function

Bastien Jean Quemener

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arXiv · 2402.09292

New proof of the Gaussian integral using the residue theorem with links to the Riemann Zeta function

Bastien Jean Quemener

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Abstract

In this paper the Gaussian integral is proven using contour integration on $\frac{1}{e^{x^2}+1}$ and linking it using a limit to said Gaussian integral. The limit is alsorelated to the Riemann Zeta function using a few manipulations. This new and original proof comes as an addition to the already many pre-existing proofs of the Gaussian integral.

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Bastien Jean Quemener. 2024-02-14. New proof of the Gaussian integral using the residue theorem with links to the Riemann Zeta function. https://arxiv.org/abs/2402.09292

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