Exact solutions of a q -discrete second Painlevé equation from its iso-monodromy deformation problem. II. Hypergeometric solutions | Zendy

Nalini Joshi | Zendy; Yang Shi | Zendy

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Exact solutions of a q -discrete second Painlevé equation from its iso-monodromy deformation problem. II. Hypergeometric solutions

Author(s) -

Nalini Joshi,

Yang Shi

Publication year - 2012

Publication title -

proceedings of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

eISSN - 1471-2946

pISSN - 1364-5021

DOI - 10.1098/rspa.2012.0224

Subject(s) - monodromy , hypergeometric distribution , hypergeometric function , mathematics , type (biology) , sequence (biology) , pure mathematics , deformation (meteorology) , representation (politics) , mathematical analysis , physics , ecology , genetics , politics , meteorology , political science , law , biology

This is the second part of our study of the solutions of aq -discrete second Painlevé equation (q -PII ) of type (A 2 +A 1 )(1) via its iso-monodromy deformation problem. In part I, we showed how to use theq -discrete linear problem associated withq -PII to find an infinite sequence of exact rational solutions. In this paper, we study the case giving rise to an infinite sequence ofq -hypergeometric-type solutions. We find a new determinantal representation of all such solutions and solve the iso-monodromy deformation problem in closed form.

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