The Virial Series of the Ideal Bose-Einstein Gas

Abstract

It is suggested that the ideal Bose-Einstein gas be used as the prototype of an imperfect gas in investigating a possible connection between divergence of the virial series and the condensation phenomenon. An explicit expression is obtained for the virial coefficients in this case. Obtaining the radius of convergence of this series appears to be a formidable mathematical problem, and only a lower bound for this radius is established. It is conjectured, however, that the radius of convergence is infinite.