Speaker
石川雅雄 (岡山大学自然科学研究科)
Date
October 7, 13:45-14:35
Title
Hankel type Pfaffians and the associated Jacobi polynomials
Abstract
Recently we studied a method to evaluate Hankel type hyperpfaffians by reducing it to Selberg integrals using hyperdeterminant version of de Bruijin's formula (see arXiv: 2008.09776). This talk is about the continuation of this work. We had some conjectures in the last section. Hankel determinants are usually closely related to moment sequences of orthogonal polynomials. Gessel and Xin studied the Hankel determinants of the moment sequence whose generating function can be written as a ratio of Gauss's hypergeometric series. Here we show that Hankel Pfaffians of this kind of moment sequences are closely related to the associated Jacobi polynomials. The weight function of the associated Jacobi polynomials is given by Wimp (also studied by Ismail and Mason). Here we report some progress on our conjectured identities. This is a joint work with Theresia Eisenkolbl and Jiang Zeng in University of Lyon I.