### Analytic solutions to the q-Painlevé equations around the origin

Ohyama, Y *(Osaka)*

Friday 03 July 2009, 14:00-14:30

Seminar Room 1, Newton Institute

#### Abstract

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.

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