 03467 Leonardo F. Guidi, Domingos H. U. Marchetti
 Convergence of Mayer Series via CauchyKowalewski Majorant
Methods with Application
(412K, Postscript)
Oct 14, 03

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. We construct majorant functions $\Phi (\beta ,z)$ for the Mayer series of
pressure satisfying a nonlinear differential equation of first
order which can be solved by the method of characteristics. The domain $%
\vert z\vert <r(\beta )$ of convergence of Mayer series is given
by the envelop of characteristics defined by the first crossing time of
whole family. For non negative potentials we derive an explicit solution in
terms of the Lambert $W$function which is related to the exponential
generating function of rooted trees $T$ as $T(x)=W(x)$. For stable
potentials the solution is majorized by a non negative potential solution.
There are many choices in this case and we used this freedon to reexamine
the ultraviolet problem of Yukawa potential. We also apply
CauchyKowalevsky theorem in order to discuss the analytic continuation of $%
\Phi (\beta ,z)$ to the complex $z$plane.
 Files:
03467.src(
03467.comments ,
03467.keywords ,
mayer9.ps )