Casorati Determinant Solutions for the Discrete Painlevé III Equation

Details Casorati Determinant Solutions for the Discrete Painlevé III Equation Casorati Determinant Solutions for the Discrete Painlevé III Equation

1994-12-15

arxiv.org/abs/solv-int/9412004v1

Physics

High Energy Physics

High Energy Physics - Theory

16 pages in LaTeX

Scientific paper

10.1063/1.531353

The discrete Painlev\'e III equation is investigated based on the bilinear formalism. It is shown that it admits the solutions expressed by the Casorati determinant whose entries are given by the discrete Bessel function. Moreover, based on the observation that these discrete Bessel functions are transformed to the $q$-Bessel functions by a simple variable transformation, we present a $q$-difference analogue of the Painlev\'e III equation.

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