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Population density techniques are statistical methods to describe large populations of spiking neurons. They describe the response of such a population to a stochastic input. These techniques are sometimes defined as the interaction of neuronal dynamics and a Poisson point process. In earlier work I showed that one can transform away neuronal dynamics, which leaves only the problem of solving the master equation for the Poisson point process. Previously, I used a numerical solution for the master equation. In this work, I will present an analytic solution, which is based on a formal solution by Sirovich (2003). I will show that using this solution for solving the population density equation results in a much faster and manifestly stable algorithm.