Hypergeometric Solutions of the $A_4^{(1)}$-Surface $q$-Painlevé IV Equation

Abstract

We consider a $q$-Painlevé IV equation which is the $A_4^{(1)}$-surface type in the Sakai's classification. We find three distinct types of classical solutions with determinantal structures whose elements are basic hypergeometric functions. Two of them are expressed by ${}_2{\phi }_1$ basic hypergeometric series and the other is given by ${}_2{\psi }_2$ bilateral basic hypergeometric series.

References in corpus (6)

• 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 $E_7^{(1)}$
• Hypergeometric $\tau$ Function of the $q$-Painlevé Systems of Type $(A_2+A_1{)}^{(1)}$
• Hypergeometric solutions to the symmetric q-Painlevé equations

Cited by in corpus (1)

• Lattice equations arising from discrete Painlevé systems. II. $A_4^{(1)}$ case