Hypergeometric Solutions for the $q$-Painlevé Equation of type $E_6^{(1)}$ by Padé Method

Abstract

The $q$-Painlevé equation of type $E_6^{(1)}$ is obtained by Padé method. Special solutions in determinant formula to the $q$-Painlevé equation is presented. A relation between Padé method and Bäcklund transformation of type $E_6^{(1)}$ is given.

23 pages, 2 figures

References in corpus (5)

• A study on the fourth q-Painlevé equation
• Hypergeometric solutions to the q-Painlevé equation of type $A_4^{(1)}$
• On a q-difference Painlevé III equation: I. Derivation, symmetry and Riccati type solutions
• Hypergeometric $\tau$-Functions of the $q$-Painlevé System of Type $E_7^{(1)}$
• A unified description of the asymmetric q-P_{v} and d-P_{iv} equations and their Schlesinger transformations

Cited by in corpus (6)

• Variations of $q$-Garnier system
• Lax pairs of discrete Painlevé equations: $(A_2+A_1{)}^{(1)}$ case
• The Padé interpolation method applied to $q$-Painlevé equations
• Lattice equations arising from discrete Painlevé systems. II. $A_4^{(1)}$ case
• A Variation of the $q$-Painlevé System with Affine Weyl Group Symmetry of Type $E_7^{(1)}$
• The Padé interpolation method applied to $q$-Painlevé equations II (differential grid version)