Hypergeometric solutions to the q-Painlevé equations

Abstract

Hypergeometric solutions to seven q-Painlevé equations in Sakai's classification are constructed. Geometry of plane curves is used to reduce the q-Painlevé equations to the three-term recurrence relations for q-hypergeometric functions.

17 pages

References in corpus (2)

• The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue
• A study on the fourth q-Painlevé equation

Cited by in corpus (4)

• Hypergeometric solutions to the q-Painlevé equation of type $A_4^{(1)}$
• Semi-classical Orthogonal Polynomial Systems on Non-uniform Lattices, Deformations of the Askey Table and Analogs of Isomonodromy
• Padé interpolation for elliptic Painlevé equation
• Point configurations, Cremona transformations and the elliptic difference Painlevé equation