# Bessel potential

In mathematics, the Bessel potential is a potential (named after Friedrich Wilhelm Bessel) similar to the Riesz potential but with better decay properties at infinity.

If s is a complex number with positive real part then the Bessel potential of order s is the operator

where Δ is the Laplace operator and the fractional power is defined using Fourier transforms.

Yukawa potentials are particular cases of Bessel potentials for in the 3-dimensional space.

## Representation in Fourier space

The Bessel potential acts by multiplication on the Fourier transforms: for each

## Integral representations

When , the Bessel potential on can be represented by

where the Bessel kernel is defined for by the integral formula [1]

Here denotes the Gamma function. The Bessel kernel can also be represented for by[2]

## Asymptotics

At the origin, one has as ,[3]

In particular, when the Bessel potential behaves asymptotically as the Riesz potential.

At infinity, one has, as , [4]