Hypergeometric Solutions to the q-Painlev\'e Equation of Type $(A_1+A_1')^{(1)}$
Exactly Solvable and Integrable Systems
2007-05-23 v1 Classical Analysis and ODEs
Abstract
A class of classical solutions to the -Painlev\'e equation of type (a -difference analog of the Painlev\'e II equation) is constructed in a determinantal form with basic hypergeometric function elements. The continuous limit of this -Painlev\'e equation to the Painlev\'e II equation and its hypergeometric solutions are discussed. The continuous limit of these hypergeometric solutions to the Airy function is obtained through a uniform asymptotic expansion of their integral representation.
Keywords
Cite
@article{arxiv.nlin/0607065,
title = {Hypergeometric Solutions to the q-Painlev\'e Equation of Type $(A_1+A_1')^{(1)}$},
author = {Taro Hamamoto and Kenji Kajiwara and Nicholas S. Witte},
journal= {arXiv preprint arXiv:nlin/0607065},
year = {2007}
}
Comments
17 pages