Approximating the Dirac distribution for Fourier analysis (Q5919273)

The Dirac distribution is often approximated by a Gaussian distribution. Here the periodic Dirac distribution is approximated by the smooth periodic \(\beta_{\pi}\)-distribution. A procedure for computing the Fourier coefficients of the \(\beta_{\pi}\)-distribution is described. The results are applied to a boundary value problem of the heat equation in a disk containing a singularity in the boundary condition.