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arXiv · 1812.11730

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

Hideshi Yamane
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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.

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Hideshi Yamane. 2018-12-31. Some trigonometric integrals and the Fourier transform of a spherically symmetric exponential function. https://arxiv.org/abs/1812.11730

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