On a class of algebraic solutions to Painlevé VI equation, its determinant formula and coalescence cascade

2002/02/21 by Tetsu Masuda, Masuda, Tetsu
Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0202044

35 pages

arxiv created 2002/02/21 · arxiv updated 2009/11/30

Abstract

A determinant formula for a class of algebraic solutions to Painlevé VI equation (P_{\rm VI}) is presented. This expression is regarded as a special case of the universal characters. The entries of the determinant are given by the Jacobi polynomials. Degeneration to the rational solutions of P_{\rm V} and P_{\rm III} is discussed by applying the coalescence procedure. Relationship between Umemura polynomials associated with P_{\rm VI} and our formula is also discussed.

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