Asymptotic behaviour of rigid-rotor partition functions

Abstract

The Euler-Maclaurin and Poisson summation formulae are used to derive an asymptotic expansion for the function Psi (a, sigma ) identical to (n+a) exp(-(n+a)2 sigma ) in powers of sigma , where 0<or=a(1. An exact formula for the remainder terms in this expansion is established. The theory of theta functions and the terminant method developed by Dingle (1973) are also applied to the problem. Finally, the results are used to investigate the high-temperature behaviour of the rigid-rotor partition functions which arise in statistical mechanics.