𝑞-Heun equation and initial-value space of 𝑞-Painlevé equation-Reference-Cited by-同舟云学术

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𝑞-Heun equation and initial-value space of 𝑞-Painlevé equation

Published:2023 Issue: Volume: Page:119-142
ISSN:0271-4132
Container-title:Recent Trends in Formal and Analytic Solutions of Diff. Equations
language:
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Author:

Sasaki Shoko,Takagi Shun,Takemura Kouichi

Abstract

We show that the q q -Heun equation and its variants appear in the linear q q -difference equations associated to some q q -Painlevé equations by considering the blow-up associated to their initial-value spaces. We obtain the firstly degenerated Ruijsenaars-van Diejen operator from the linear q q -difference equation associated to the q q -Painlevé equation of type E 8 E_8 .

Publisher

American Mathematical Society

Reference16 articles.

1. The Heun-Askey-Wilson algebra and the Heun operator of Askey-Wilson type;Baseilhac, Pascal;Ann. Henri Poincar\'{e},2019

2. A Riemann-Hilbert approach to the Heun equation;Dubrovin, Boris;SIGMA Symmetry Integrability Geom. Methods Appl.,2018

3. On linear geometric difference equations with accessory parameters;Hahn, Wolfgang;Funkcial. Ekvac.,1971

4. Algebraic transformations of ₃𝐹₂;Kato, Mitsuo;Funkcial. Ekvac.,2008

5. A 𝑞-analog of the sixth Painlevé equation;Jimbo, Michio;Lett. Math. Phys.,1996

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