TY - JOUR
T1 - Exact solutions of a q-discrete second Painlevé equation from its iso-monodromy deformation problem. II. Hypergeometric solutions
T2 - {II}. {H}ypergeometric solutions
AU - Joshi, Nalini
AU - Shi, Yang
PY - 2012/10/8
Y1 - 2012/10/8
N2 - 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.
AB - 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.
KW - discrete Painlevé equation
KW - iso-mondromy deformation
KW - special solutions
KW - Discrete Painlevé equation
KW - Iso-monodromy deformation
KW - Special solutions
UR - http://purl.org/au-research/grants/ARC/DP0985615
UR - http://purl.org/au-research/grants/ARC/DP110102001
UR - http://www.scopus.com/inward/record.url?scp=84866378202&partnerID=8YFLogxK
U2 - 10.1098/rspa.2012.0224
DO - 10.1098/rspa.2012.0224
M3 - Article
SN - 1364-5021
VL - 468
SP - 3247
EP - 3264
JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
IS - 2146
ER -