Abstract
This paper presents \textsc{hankel}, a pure-python code for solving Hankel-type integrals and transforms. Such transforms are common in the physical sciences, especially appearing as the radial solution to angularly symmetric Fourier Transforms in arbitrary dimensions. The code harnesses the advantages of solving such transforms via the one-dimensional Hankel transform -- an increase in conceptual simplicity and efficiency -- and implements them in the user-friendly and flexible Python language. We discuss several limitations of the adopted method, and point to the code's extensive documentation for further examples.
Highlights
As an example, in cosmology, the density field of the Universe is expected to be isotropic
The NASA Astronomical Data Service yields over 700 refereed articles including the term “hankel transform”, in fields as diverse as astronomy, geophysics, fluid mechanics, electrodynamics, thermodynamics and acoustics
Due to the isotropy of the field, these can be related by an angularly symmetric Fourier transform, which is more expressed as a Hankel transform (Szapudi, Pan, Prunet, & Budavári, 2005)
Summary
In cosmology, the density field of the Universe is expected to be isotropic. The Hankel transform is a one-dimensional functional transform involving a Besselfunction kernel. It is the radial solution to an angularly symmetric Fourier transform of any dimension, rendering it very useful in several fields of application.
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