This article is cited in 6 papers

Analytic continuation of mayer and virial expansions

G. I. Kalmykov

All-Union Extra-Mural Institute of Food Industry

Abstract: Functions that under certain assumptions are analytic continuations of Mayer expansions are found. It is shown that there exists a positive number $\rho_1$ satisfying the following conditions: 1) tor any interval of the form $[0,\rho_1(1-\varepsilon)]$, where $0<\varepsilon<1$, there exists a region containing this interval in which there is defined a single-valued analytic single-sheeted function that is the inverse with respect to the analytic continuation $f(z)$ of the Mayer expansion which represents the density as a function of the activity; 2) there does not exist a single-valued analytic function that would be the inverse with respect to the function $f(z)$ in a certain region containing the interval $[0,\rho_1]$. It is shown to be possible to continue analytically the virial expansion along the path $[0,\rho_1(1-\varepsilon)]$, where $0<\varepsilon<1$, and impossible to do this along the pathl $[0,\rho_1]$. An equation that determines a positive number $z_1$ such that $\rho_1=f(z_1)$ is found.

Received: 03.01.1992

 English version: Theoretical and Mathematical Physics, 1992, 92:1, 791–798

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