Some trigonometric integrals and the Fourier transform of a spherically symmetric exponential function
Classical Analysis and ODEs
2019-01-01 v1
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.
Keywords
Cite
@article{arxiv.1812.11730,
title = {Some trigonometric integrals and the Fourier transform of a spherically symmetric exponential function},
author = {Hideshi Yamane},
journal= {arXiv preprint arXiv:1812.11730},
year = {2019}
}
Comments
6 pages