Special Functions of the Isomonodromy Type, Rational Transformations of Spectral Parameter, and Algebraic Solutions of the Sixth Painlev\'e Equation

摘要

We discuss relations which exist between analytic functions belonging to therecently introduced class of special functions of the isomonodromy type(SFITs). These relations can be obtained by application of some simpletransformations to auxiliary ODEs with respect to a spectral parameter whichassociated with each SFIT. We consider two applications of rationaltransformations of the spectral parameter in the theory of SFITs. One of themost striking applications which is considered here is an explicit constructionof algebraic solutions of the sixth Painlev\'e equation.