Geodesic
Analytic continuation of mayer and virial expansions
Teoretičeskaâ i matematičeskaâ fizika, Tome 92 (1992) no. 1, pp. 139-149 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {Analytic continuation of mayer and virial expansions},
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     pages = {139--149},
     year = {1992},
     volume = {92},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1992_92_1_a12/}
}
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G. I. Kalmykov. Analytic continuation of mayer and virial expansions. Teoretičeskaâ i matematičeskaâ fizika, Tome 92 (1992) no. 1, pp. 139-149. http://geodesic.mathdoc.fr/item/TMF_1992_92_1_a12/

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