Casorati Determinant Solutions for the Discrete Painlevé-II Equation

Abstract

We present a class of solutions to the discrete Painlevé-II equation for particular values of its parameters. It is shown that these solutions can be expressed in terms of Casorati determinants whose entries are discrete Airy functions. The analogy between the $\tau$ function for the discrete P$_{\rm \romanno2}$ and the that of the discrete Toda molecule equation is pointed out.

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