# Some trigonometric integrals and the Fourier transform of a spherically symmetric exponential function

## TL;DR

This paper presents a simplified method for computing the Fourier transform of a spherically symmetric exponential function, leveraging symmetry and homogeneity to reduce complexity.

## Contribution

It introduces a more straightforward approach to evaluate the Fourier transform of spherically symmetric exponential functions using polar coordinates and symmetry properties.

## Key findings

- Simplified Fourier transform calculation method
- Reduction to rational trigonometric integral
- Connection to harmonic function Fourier representations

## Abstract

We calculate the Fourier transform of a spherically symmetric exponential function. Our evaluation is much simpler than the known one. We use the polar coordinates and reduce the Fourier transform to the integral of a rational function of trigonometric functions. Its evaluation turns out to be much easier than expected because of homogeneity and a hidden symmetry. Relationship with a Fourier integral representation formula for harmonic functions is explained.