The Padé interpolation method applied to $q$-Painlevé equations

Abstract

We establish interpolation problems related to all the $q$-Painlevé equations of types from $E_7^{(1)}$ to $(A_2+A_1{)}^{(1)}$. By solving those problems, we can derive the evolution equations, the scalar Lax pairs and the determinant formulae of special solutions for the corresponding $q$-Painlevé equations.

16 pages

References in corpus (5)

• Lax forms of the $q$-Painlevé equations
• Hypergeometric solutions to the q-Painlevé equation of type $A_4^{(1)}$
• Hypergeometric $\tau$-Functions of the $q$-Painlevé System of Type $E_7^{(1)}$
• Construction of a Lax Pair for the $E_6^{(1)}$ $q$-Painlevé System
• Hypergeometric $\tau$ Function of the $q$-Painlevé Systems of Type $(A_2+A_1{)}^{(1)}$

Cited by in corpus (4)

• Variations of $q$-Garnier system
• Lax pairs of discrete Painlevé equations: $(A_2+A_1{)}^{(1)}$ case
• Lattice equations arising from discrete Painlevé systems. II. $A_4^{(1)}$ case
• The Padé interpolation method applied to $q$-Painlevé equations II (differential grid version)