Exact solution for two-dimensional Coulomb matrix elements
  Exact analytic expression is derived for the matrix elements of the Coulomb interaction in two dimensions in the form of a closed finite sum expression. The orthonormal complete set of eigenfunctions of the harmonic oscillator is used as the basis for spanning real space. Several recurrence relations have been found in order to simplify the task of calculating the usually vast amount of elements required for any computer simulation. 
Jaime Zaratiegui