Ultradiscrete limit of Bessel function type solutions of the Painlev\'{e} III equation
Exactly Solvable and Integrable Systems
2014-09-08 v1
Abstract
An ultradiscrete analog of the Bessel function is constructed by taking the ultradiscrete limit for a -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.
Keywords
Cite
@article{arxiv.1409.1684,
title = {Ultradiscrete limit of Bessel function type solutions of the Painlev\'{e} III equation},
author = {Shin Isojima},
journal= {arXiv preprint arXiv:1409.1684},
year = {2014}
}