Special function solutions of the discrete Painlevé equations

DOI10.1016/S0898-1221(01)00180-8zbMath0994.33500OpenAlexW2018357620MaRDI QIDQ1600404

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

Publication date: 13 June 2002

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0898-1221(01)00180-8

zbMATH Keywords

affine Weyl groupsPainlevé equationdiscrete special function

Mathematics Subject Classification ID

Related Items (18)

The Padé interpolation method applied to \(q\)-Painlevé equations. II (differential grid version) ⋮ Hypergeometric \(\tau\) functions of the \(q\)-Painlevé systems of types \(A_4^{(1)}\) and \((A_1+A_1')^{(1)}\) ⋮ On a q-Difference Painlevé III Equation: I. Derivation, Symmetry and Riccati Type Solutions ⋮ Lattice equations arising from discrete Painlevé systems. I. (A2 + A1)(1) and (A1+A1′)(1) cases ⋮ Riccati solutions of discrete Painlevé equations with Weyl group symmetry of type E8(1) ⋮ Special functions arising from discrete Painlevé equations: a survey ⋮ Schwarzian derivative and Ermakov equation on a time scale ⋮ A \(3 \times 3\) Lax form for the \(q\)-Painlevé equation of type \(E_6\) ⋮ A variation of the \(q\)-Painlevé system with affine Weyl group symmetry of type \(E_7^{(1)}\) ⋮ Unique special solution for discrete Painlevé II ⋮ Transcendence of solutions of \(q\)-Painlevé equation of type \({A^{(1)}_{6}}\) ⋮ An ultrametric version of the Maillet-Malgrange theorem for nonlinear $q$-difference equations ⋮ Geometric aspects of Painlevé equations ⋮ The Padé interpolation method applied to \(q\)-Painlevé equations ⋮ An ultradiscrete matrix version of the fourth Painlevé equation ⋮ Discrete orthogonal polynomials with hypergeometric weights and Painlevé VI ⋮ On a q-Difference Painlevé III Equation: II. Rational Solutions ⋮ The Padé interpolation method applied to additive difference Painlevé equations

Cites Work

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• A geometrical description of the discrete Painlevé VI and V equations
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