New proof of the Gaussian integral using the residue theorem with links to the Riemann Zeta function
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914679142481920 |
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| author | Quemener, Bastien Jean |
| author_facet | Quemener, Bastien Jean |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_09292 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New proof of the Gaussian integral using the residue theorem with links to the Riemann Zeta function Quemener, Bastien Jean Complex Variables 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. |
| title | New proof of the Gaussian integral using the residue theorem with links to the Riemann Zeta function |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2402.09292 |