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This book is the first comprehensive treatment of Painlev differential
equations in the complex plane. Starting with a rigorous presentation for
the meromorphic nature of their solutions, the Nevanlinna theory will be
applied to offer a detailed exposition of growth aspects and value distri-
bution of Painlev transcendents. The subsequent main part of the book
is devoted to topics of classical background such as representations and
expansions of solutions, solutions of special type like rational and special
transcendental solutions, Bcklund transformations and higher order
analogues, treated separately for each of these six equations. The final
chapter offers a short overview of applications of Painlev equations,
including an introduction to their discrete counterparts.
Due to the present important role of Painlev equations in physical ap-
plications, this monograph should be of interest to mathematicians and
physicists both in research and in postgraduate studies.