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Analytic solutions to the q-Painlev equations around the origin

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We study special solutions to the q-Painleve equations, which are analytic around the origin or the infinity. As the same as continuous Painleve equations, we have a finite number of such solutions. The q-Painleve equations are epressed as a connection preserving deformation (Jimbo and Sakai in q-PVI; M. Murata in other cases). We can determine the connection data for analytic solutions. In the case of q-PVI, the connection data reduces to Heine’s basic hypergeometric functions.

This talk is part of the Isaac Newton Institute Seminar Series series.

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