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A $q$-anaolg of the sixth Painlevé equation

Michio Jimbo·Hidetaka Sakai
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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.

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Michio Jimbo, Hidetaka Sakai. 1995-08-15. A $q$-anaolg of the sixth Painlevé equation. https://doi.org/10.1007/bf00398316

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