On a q-difference Painlevé III equation: I. Derivation, symmetry and Riccati type solutions

Abstract

A q-difference analogue of the Painlevé III equation is considered. Its derivations, affine Weyl group symmetry, and two kinds of special function type solutions are discussed.

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References in corpus (1)

• A study on the fourth q-Painlevé equation

Cited by in corpus (12)

• Geometric Aspects of Painlevé Equations
• Hypergeometric solutions to the q-Painlevé equation of type $A_4^{(1)}$
• On a q-difference Painlevé III equation: II. Rational solutions
• Bilinear equations and $q$-discrete Painlevé equations satisfied by variables and coefficients in cluster algebras
• Projective reduction of the discrete Painlevé system of type $(A_2+A_1{)}^{(1)}$
• Hypergeometric Solutions for the $q$-Painlevé Equation of type $E_6^{(1)}$ by Padé Method
• Hypergeometric $\tau$ Function of the $q$-Painlevé Systems of Type $(A_2+A_1{)}^{(1)}$
• Symmetries and Special Solutions of Reductions of the Lattice Potential KdV Equation
• Hypergeometric $\tau$ Functions of the $q$-Painlevé Systems of Types $A_4^{(1)}$ and $(A_1+A_1^{\prime }{)}^{(1)}$
• Hypergeometric Solutions of the $A_4^{(1)}$-Surface $q$-Painlevé IV Equation
• Isomonodromic deformation of q-difference equations and confluence
• Symmetries in Connection Preserving Deformations