Special functions arising from discrete Painlevé equations: a survey
DOI10.1016/j.cam.2006.01.034zbMath1123.39013OpenAlexW2049544722MaRDI QIDQ875350
Publication date: 13 April 2007
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cam.2006.01.034
special functionsdiscrete Painlevé equationbasic hypergeometric serieshypergeometric solutions\(q\)-Painlevé equations
Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Discrete version of topics in analysis (39A12) Difference equations, scaling ((q)-differences) (39A13) Painlevé-type functions (33E17)
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- Affine Weyl groups, discrete dynamical systems and Painlevé equations
- Rational solutions of the fifth Painlevé equation
- Rational surfaces associated with affine root systems and geometry of the Painlevé equations
- Monodromy of certain Painlevé-VI transcendents and reflection groups
- Special function solutions of the discrete Painlevé equations
- The Painlevé property. One century later
- Classical transcendental solutions of the Painlevé equations and their degeneration
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- A \(q\)-analog of the sixth Painlevé equation
- Bilinear discrete Painleve equations
- The Associated Askey-Wilson Polynomials
- Discrete versions of the Painlevé equations
- Do integrable mappings have the Painlevé property?
- 10E9solution to the elliptic Painlev equation
- Riccati solutions of discrete Painlevé equations with Weyl group symmetry of type E8(1)
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