# (p.521) A Fourier transform and Fourier series

# (p.521) A Fourier transform and Fourier series

# A.1 Fourier series of lattice periodic functions

Let *v*(**r**) = *v*(**r** + **R**) be a lattice periodic function. Its expansion in a Fourier series is

*V*

_{0}, and

**K**is a vector of the reciprocal lattice.

# A.3 Fourier transform in two dimensions

In two dimensions the Fourier transform of a function is given by

*U*(

**r**) possesses radial symmetry, i.e. it depends only on

*r*= |

**r**|, then

We talk about the Fourier–Bessel expansion, because the *J* _{0}(*kr*) are Bessel functions.

**Fourier transform of the Coulomb potentials.** The two-dimensional Fourier transform of the Coulomb potential