Asymptotic Expansion for Erlang Loss Function and Its Derivative

This paper reveals the general structure of the asymptotic expansion for the Erlang loss function and its derivative. A recursive formula for the coefficients in the expansion is given and some of numerical examples are presented. The truncation error of the expansion is estimated and charts for calculation with the error less than 0.1 percent are shown. The present formula facilitates the calculation by saving the computation time, and it is useful for the optimization problems of switching systems and other applications.