A short study of generalized Dirichlet Integrals via tempered distributions

TL;DR

This paper employs Fourier theory of tempered distributions to derive a novel formula for Dirichlet-like integrals efficiently, showcasing an innovative methodology that simplifies complex calculations.

Contribution

It introduces a new formula for Dirichlet-like integrals using tempered distributions and demonstrates an efficient derivation method.

Findings

Derived an apparently unknown formula for Dirichlet-like integrals.

Showcased an efficient method using Fourier theory of tempered distributions.

Highlighted the originality of the derivation approach.

Abstract

In the present article, the author uses Fourier theory of tempered distributions (generalized functions) in deriving a formula for Dirichlet-like integrals. The applied method is remarkably efficient and allows a solution in a few calculational steps. The interest of the present article lies not only in the derivation of an appearently unknown formula but also in the original methodology of its derivation.