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Joshi N, Shi Y. Exact solutions of a
q
-discrete second Painlevé equation from its iso-monodromy deformation problem. II. Hypergeometric solutions. Proc Math Phys Eng Sci 2012. [DOI: 10.1098/rspa.2012.0224] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
This is the second part of our study of the solutions of a
q
-discrete second Painlevé equation (
q
-P
II
) of type (
A
2
+
A
1
)
(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.
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Affiliation(s)
- Nalini Joshi
- School of Mathematics and Statistics, The University of Sydney, New South Wales 2006, Australia
| | - Yang Shi
- School of Mathematics and Statistics, The University of Sydney, New South Wales 2006, Australia
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