Hypergeometric solutions to the q-Painlevé equation of type $A_4^{(1)}$

Abstract

We consider the q-Painlevé equation of type $A_4^{(1)}$ (a version of q-Painlevé V equation) and construct a family of solutions expressible in terms of certain basic hypergeometric series. We also present the determinant formula for the solutions.

arXiv comment16 pages, IOP style

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• Exact Solutions with Two Parameters for an Ultradiscrete Painlevé Equation of Type $A_6^{(1)}$
• Hypergeometric $\tau$ Function of the $q$-Painlevé Systems of Type $(A_2+A_1{)}^{(1)}$
• The Padé interpolation method applied to $q$-Painlevé equations
• A Class of Special Solutions for the Ultradiscrete Painlevé II Equation
• The Padé interpolation method applied to $q$-Painlevé equations II (differential grid version)
• Hypergeometric $\tau$ Functions of the $q$-Painlevé Systems of Types $A_4^{(1)}$ and $(A_1+A_1^{\prime }{)}^{(1)}$
• Studies on the discrete integrable equations over finite fields
• The space of initial conditions and the property of an almost good reduction in discrete Painleve II equations over finite fields
• A connection formula between the Ramanujan function and the $q$-Airy function
• On local solutions of the Ramanujan equation and their connection formulae
• Hypergeometric Solutions of the $A_4^{(1)}$-Surface $q$-Painlevé IV Equation
• The Stokes phenomenon for the Ramanujan's $q$-difference equation and its higher order extension
• Ultradiscrete limit of Bessel function type solutions of the Painlevé III equation
• Discrete Painleve equations and discrete KdV equation over finite fields