Ultradiscrete limit of Bessel function type solutions of the Painlev\'e III equation
Abstract
An ultradiscrete analog of the Bessel function is constructed by taking the ultradiscrete limit for a q-difference analog of the Bessel function. Then, a direct relationship between a class of special solutions for the ultradiscrete Painlev\'e III equation and those of the discrete Painlev\'e III equation which have a determinantal structure is established.
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