Construction of Hypergeometric Solutions to the q-Painlevé Equations

2005/01/31 by Kenji Kajiwara, Kajiwara, Kenji, Tetsu Masuda +7
Computer Science · Mathematics · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical functions and polynomials #Nonlinear Waves and Solitons #Polynomial and algebraic computation #math.CA #nlin.SI

paper · pdf · doi:10.48550/arxiv.nlin/0501051

17 pages

arxiv created 2005/01/31 · openalex publication_date 2005/01/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Hypergeometric solutions to the q-Painlevé equations are constructed by direct linearization of disrcrete Riccati equations. The decoupling factors are explicitly determined so that the linear systems give rise to q-hypergeometric equations.

Citations

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue

Related

• Hypergeometric solutions to the q-Painlevé equations
• Hypergeometric Solutions to the q-Painlevé Equation of Type (A₁+A₁')⁽¹⁾
• Hypergeometric solutions to the symmetric q-Painlevé equations
• Some Rational Solutions to Painleve' VI
• Hypergeometric solutions for variants of the q-hypergeometric equation