Infinite Analysis Seminar Tokyo

Seminar information archive ～04/28｜Next seminar｜Future seminars 04/29～

Date, time & place Saturday 13:30 - 16:00 117Room #117 (Graduate School of Math. Sci. Bldg.)

2023/04/24

16:00-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)
Takahiko Nobukawa (Kobe University )
Euler type integral formulas and hypergeometric solutions for
variants of the $q$ hypergeometric equations.
(Japanese)
[ Abstract ]
We know that Papperitz's differential equation is essentially obtained from
Gauss' hypergeometric equation by applying a Moebius transformation,
implying that we have Euler type integral formulas or hypergeometric solutions.
The variants of the $q$ hypergeometric equations, introduced by
Hatano-Matsunawa-Sato-Takemura (Funkcial. Ekvac.,2022), are second order
$q$-difference systems which can be regarded as $q$ analoges of Papperitz's equation.
This motivates us for deriving Euler type integral formulas and hypergeometric solutions
for the pertinent $q$-difference systems. If time admits, I explain
the relation with $q$-analogues of Kummer's 24 solutions,
or the variants of multivariate $q$-hypergeometric functions.
This talk is based on the collaboration with Taikei Fujii.