Padé Interpolation for Elliptic Painlevé Equation

DOI10.1007/978-1-4471-4863-0_18zbMath1277.33020arXiv1204.0294OpenAlexW11710126MaRDI QIDQ2842065

Satoshi Tsujimoto, Yasuhiko Yamada, Masatoshi Noumi

Publication date: 31 July 2013

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1204.0294

zbMATH Keywords

Lax pairinterpolation problemcontiguity relationsdeterminant formulaeelliptic Painlevé equation

Mathematics Subject Classification ID

Other functions coming from differential, difference and integral equations (33E30) Difference equations, scaling ((q)-differences) (39A13)

Related Items (18)

The Padé interpolation method applied to \(q\)-Painlevé equations. II (differential grid version) ⋮ Theory and applications of the elliptic Painlevé equation ⋮ An elliptic Garnier system ⋮ An elliptic Garnier system from interpolation ⋮ On a novel representation of discrete Painlevé equations ⋮ A variation of the \(q\)-Painlevé system with affine Weyl group symmetry of type \(E_7^{(1)}\) ⋮ Multiplicative equations related to the affine Weyl group E8 ⋮ Lattice equations arising from discrete Painlevé systems: II. ${A}_{4}^{(1)}$ case ⋮ Singularity analysis for difference Painlevé equations associated with the affine Weyl groupE₈ ⋮ Geometric aspects of Painlevé equations ⋮ Some algebraic properties of Hermite-Padé polynomials ⋮ On the limits of discrete Painlevé equations associated with the affine Weyl group E8 ⋮ The Padé interpolation method applied to \(q\)-Painlevé equations ⋮ 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 ⋮ The elliptic Painlevé Lax equation vs. van Diejen's 8-coupling elliptic Hamiltonian

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Determinant solutions of the nonautonomous discrete Toda equation associated with the deautonomized discrete KP hierarchy
• Hypergeometric \(\tau \)-functions of the \(q\)-Painlevé system of type \(E_{8}^{(1)}\)
• A Lax formalism for the elliptic difference Painlevé equation
• Rational surfaces associated with affine root systems and geometry of the Painlevé equations
• Integrable mappings and soliton equations
• Painlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomials
• A \(q\)-analog of the sixth Painlevé equation
• Spectral transformation chains and some new biorthogonal rational functions
• An affine Weyl group approach to the eight-parameter discrete Painlevé equation
• Lax Formalism for q-Painleve Equations with Affine Weyl Group Symmetry of Type EFormula
• New Expressions for Discrete Painlevé Equations
• Essays on the theory of elliptic hypergeometric functions
• First order analytic difference equations and integrable quantum systems
• ₁₀E₉solution to the elliptic Painlev  equation
• Riccati solutions of discrete Painlevé equations with Weyl group symmetry of type E8(1)
• Pade Method to Painleve Equations

This page was built for publication: Padé Interpolation for Elliptic Painlevé Equation