The Padé interpolation method applied to \(q\)-Painlevé equations

DOI10.1007/s11005-015-0749-yzbMath1323.39007arXiv1409.3932OpenAlexW3099978347MaRDI QIDQ490738

Hidehito Nagao

Publication date: 28 August 2015

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.3932

zbMATH Keywords

Padé methodevolution equationsdeterminant formulaediscrete \(q\)-Painlevé equationPadé interpolationscalar Lax pairs

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Padé approximation (41A21) Discrete version of topics in analysis (39A12) Difference equations, scaling ((q)-differences) (39A13)

Related Items (6)

The Padé interpolation method applied to \(q\)-Painlevé equations. II (differential grid version) ⋮ A variation of the \(q\)-Painlevé system with affine Weyl group symmetry of type \(E_7^{(1)}\) ⋮ Variations of theq-Garnier system ⋮ Hermite-Padé approximation, isomonodromic deformation and hypergeometric integral ⋮ The Padé interpolation method applied to additive difference Painlevé equations ⋮ Study of <i>q</i>-Garnier System by Padé Method

Cites Work

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• Construction of a Lax pair for the \(E_{6}^{(1)} \)q-Painlevé system
• Hypergeometric solutions for the \(q\)-Painlevé equation of type \({E^{(1)}_6}\) by the Padé method
• Hypergeometric \(\tau \) functions of the \(q\)-Painlevé systems of type \((A_{2}+A_{1})^{(1)}\)
• Rational surfaces associated with affine root systems and geometry of the Painlevé equations
• Special function solutions of the discrete Painlevé equations
• Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials
• A \(q\)-analog of the sixth Painlevé equation
• On a novel \(q\)-discrete analogue of the Painlevé VI equation
• Padé Interpolation for Elliptic Painlevé Equation
• Lax Formalism for q-Painleve Equations with Affine Weyl Group Symmetry of Type EFormula
• Lax form of theq-Painlevé equation associated with theA⁽¹⁾₂surface
• A q-Analog of the Garnier System
• Lax forms of theq-Painlevé equations
• Casorati determinant solutions for theq-difference sixth Painlevé equation
• A study on the fourthq-Painlevé equation
• Recurrence coefficients for discrete orthonormal polynomials and the Painlevé equations
• Pade Method to Painleve Equations
• Hypergeometric solutions to theq-Painlevé equation of typeA⁽¹⁾₄
• Asymmetric discrete Painlevé equations

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