We deal with the connection problem on the Ramanujan equation between
around the origin and around the infinity. In the fundamental system of
solutions around the origin, a divergent basic hypergeometric series
appears. We use the q-Borel-Laplace transformations to obtain the
asymptotic expansion of the divergent series. Our conclusion also shows a
new example of the q-Stokes coefficient.
16:30〜 Davide Guzzetti（トリエステ・SISSA）
タイトル：A Review of the Sixth Painleve equation
ABSTRACT: The isomonodromy deformation method provides a unitary
description of the critical behaviors of the solutions of the Painleve
6 equation, their connection formulae and the asymptotic distribution of
the poles close to a critical point.
I will discuss the results known on the subject, including those which
I have obtained during my stay in RIMS as a COE fellow (2004-8), and in
KIAS in Seoul (2010-11).
The purpose of the talk is to introduce a table of Painleve 6
transcendents, which will be presented at the workshop "Various aspects
of the Painleve equations", RIMS, Nov 26-30.
arXiv:1108.3401 (Nonilinearity 25 3235-3276, 2012)
タイトル： Quantum Painleve systems from hypergeometric integrals