A $q$-anaolg of the sixth Painlevé equation

Abstract

A $q$-difference analog of the sixth Painlevé equation is presented. It arises as the condition for preserving the connection matrix of linear $q$-difference equations, in close analogy with the monodromy preserving deformation of linear differential equations. The continuous limit and special solutions in terms of $q$-hypergeometric functions are also discussed.

8 pages, LaTeX file (Two misprints corrected)

References in corpus (2)

• Linearization And Solutions Of The Discrete Painlevé-III Equation
• Casorati Determinant Solutions for the Discrete Painlevé-II Equation

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