CASORATI DETERMINANT SOLUTIONS FOR THE DISCRETE PAINLEVE-III EQUATION

The discrete Painleve III equation is investigated based on the biline ar formalism. It is shown that it admits the solutions expressed by th e Casorati determinant whose entries are given by the discrete Bessel functions. Moreover, based on the observation that these discrete Bess el functions are transformed to the q-Bessel functions by a simple var iable transformation, we present a q-difference analog of the Painleve III equation. (C) 1995 American Institute of Physics.