Exact solutions of a q-discrete second Painlevé equation from its iso-monodromy deformation problem. II. Hypergeometric solutions: {II}. {H}ypergeometric solutions

Nalini Joshi, Yang Shi

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

This is the second part of our study of the solutions of a q -discrete second Painlevé equation (q-PII)of type (A2 + A1)(1) via its iso-monodromy deformation problem. In part I, we showed how to use the q-discrete linear problem associated with q-P II to find an infinite sequence of exact rational solutions. In this paper, we study the case giving rise to an infinite sequence of q-hypergeometric-type solutions. We find a new determinantal representation of all such solutions and solve the iso-monodromy deformation problem in closed form.

Original languageEnglish
Pages (from-to)3247-3264
Number of pages18
JournalPROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
Volume468
Issue number2146
DOIs
Publication statusPublished - 8 Oct 2012
Externally publishedYes

Keywords

  • discrete Painlevé equation
  • iso-mondromy deformation
  • special solutions
  • Discrete Painlevé equation
  • Iso-monodromy deformation
  • Special solutions

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