Hankel determinants and Jacobi continued fractions for $q$-Euler numbers
Number Theory
2023-05-16 v2
Abstract
The -analogs of Bernoulli and Euler numbers were introduced by Carlitz. Similar to the recent results on the Hankel determinants for the -Bernoulli numbers established by Chapoton and Zeng, we determine parallel evaluations for the -Euler numbers. It is shown that the associated Favard-type orthogonal polynomials for -Euler numbers are given by a specialization of the big -Jacobi polynomials, thereby leading to their corresponding Jacobi continued fraction expression, which eventually serves as a key to our determinant evaluations.
Keywords
Cite
@article{arxiv.2305.06623,
title = {Hankel determinants and Jacobi continued fractions for $q$-Euler numbers},
author = {Shane Chern and Lin Jiu},
journal= {arXiv preprint arXiv:2305.06623},
year = {2023}
}