Ultradiscrete limit of Bessel function type solutions of the Painlevé 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 Painlevé III equation and those of the discrete Painlevé III equation which have a determinantal structure is established.

References in corpus (2)

• Hypergeometric solutions to the q-Painlevé equation of type $A_4^{(1)}$
• A Class of Special Solutions for the Ultradiscrete Painlevé II Equation