### The q-Painlevé equations arising from the q-interpolation problems

**Yamada, Y ***(Kobe University)*

Tuesday 09 July 2013, 10:00-10:30

Seminar Room 1, Newton Institute

#### Abstract

For the polynomials P(x), Q(x) obtained by a Padé (or Chauchy-Jacobi) interpolation:
Y (xi) = P(xi)=Q(xi), we consider the contiguity relations satisfied by the functions P(x) and Y (x)Q(x). In a suitable setup of the interpolation problem, the contiguity relations can be interpreted as a Lax pair for a discrete Painlevé equation. In this sense, the Padé interpolation order a cheap way to get a Lax pair of discrete Painlevé equations together with their special solutions. In this talk, I will discuss this method in some examples of the q-Painlevé equations.

#### Presentation

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