The ε-algorithm allows to detect Dirac delta functions Original Research Article

The ε-algorithm is well known as a numerical tool for accelerating the convergence of sequences. It is shown empirically that this property holds for convergent series in the general sense of distributions. This means that, at singular points, the ε-algorithm also accelerates the divergence, and clearly reveals the presence of delta functions as well as other singularities such as 1/x, step functions …. As an example, the solution of an integral equation in a problem of electrostatics, developed as a series of Legendre polynomials, has been analyzed by the ε-algorithm.