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

Bastien Jean Quemener

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.

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

Abstract

In this paper the Gaussian integral is proven using contour integration on 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.
Paper Structure (3 sections, 70 equations, 1 figure)

This paper contains 3 sections, 70 equations, 1 figure.

Table of Contents

  1. The proof
  2. Additional formulas and link to Riemann Zeta
  3. References

Figures (1)

  • Figure 1: The contour $G$ in the complex plane