NOVEL REPRESENTATION OF EXPONENTIAL FUNCTIONS OF POWER-SERIES WHICH ARISE IN STATISTICAL-MECHANICS AND POPULATION-GENETICS

We use the convolution power of infinite sequences to obtain a novel representation of exponential functions of power series which often arise in statistical mechanics. We thus obtain new formulas for the configuration and cluster integrals of pairwise interacting systems of molecules in an imperfect gas. We prove that the asymptotic behaviour of the Luria-Delbruck distribution is p(n) approximately cn-2. We derive a new, simple and computationally efficient recursion relation for p(n).