Painlevé Differential Equations in the Complex Plane (De by Valerii I. Gromak,Ilpo Laine,Shun Shimomura

By Valerii I. Gromak,Ilpo Laine,Shun Shimomura

This ebook is the 1st accomplished remedy of Painlevé differential equations within the complicated airplane. beginning with a rigorous presentation for the meromorphic nature in their ideas, the Nevanlinna conception should be utilized to provide an in depth exposition of development elements and cost distribution of Painlevé transcendents. the next major a part of the e-book is dedicated to themes of classical history reminiscent of representations and expansions of suggestions, options of targeted kind like rational and specified transcendental suggestions, Bäcklund modifications and better order analogues, taken care of individually for every of those six equations. the ultimate bankruptcy deals a quick evaluation of functions of Painlevé equations, together with an advent to their discrete opposite numbers. as a result of the current very important function of Painlevé equations in actual functions, this monograph might be of curiosity to researchers in either arithmetic and physics and to graduate scholars attracted to mathematical physics and the speculation of differential equations.

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