Special functions as solutions to discrete Painlevé equations.

DOI10.1016/S0377-0427(03)00635-6zbMath1107.39303MaRDI QIDQ1414353

T. Tamizhmani, K. M. Tamizhmani, Basile Grammaticos, Alfred Ramani

Publication date: 20 November 2003

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

Painlevé equationssecond-order discrete equations

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Discrete version of topics in analysis (39A12) Painlevé-type functions (33E17)

Cites Work

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• From continuous to discrete Painlevé equations
• Rational surfaces associated with affine root systems and geometry of the Painlevé equations
• The hunting for the discrete Painlevé equations
• Integrable mappings and soliton equations. II
• Discrete Painlevé equations: coalescences, limits and degeneracies
• On a novel \(q\)-discrete analogue of the Painlevé VI equation
• An affine Weyl group approach to the eight-parameter discrete Painlevé equation
• Coalescence cascades and special-function solutions for the continuous and discrete Painlevé equations
• Discrete versions of the Painlevé equations
• Special function solutions for asymmetric discrete Painlevé equations
• Asymmetric discrete Painlevé equations

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