Elliptic and Hyperelliptic Solutions of Discrete Painlev\'e I and Its Extensions to Higher Order Difference Equations
Abstract
The solutions of the discrete Painlev\'e equation I were constructed in terms of elliptic and hyperelliptic functions for algebraic curves of genera one and two. For the case of genus two, there appear higher order difference equations which naturally contain the discrete Painlev\'e equation I as a special case.
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