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The q-Painlev equations arising from the q-interpolation problems

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If you have a question about this talk, please contact Mustapha Amrani.

Discrete Integrable Systems

For the polynomials P(x), Q(x) obtained by a Pad (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 Painlev equation. In this sense, the Pad interpolation order a cheap way to get a Lax pair of discrete Painlev equations together with their special solutions. In this talk, I will discuss this method in some examples of the q-Painlev equations.

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

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