no. G2
Article de recherche - Théorie des nombres
Hankel determinants and Jacobi continued fractions for q-Euler numbers
Chern, Shane1 orcid ; Jiu, Lin2 orcid 
1Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, B3H 4R2, Canada
2Zu Chongzhi Center for Mathematics and Computational Sciences, Duke Kunshan University, Kunshan, Suzhou, Jiangsu Province, 215316, PR China
Comptes Rendus. Mathématique, Tome 362 (2024) no. G2, pp. 203-216

The q-analogs of Bernoulli and Euler numbers were introduced by Carlitz in 1948. Similar to recent results on the Hankel determinants for the q-Bernoulli numbers established by Chapoton and Zeng, we perform a parallel analysis for the q-Euler numbers. It is shown that the associated orthogonal polynomials for q-Euler numbers are given by a specialization of the big q-Jacobi polynomials, thereby leading to their corresponding Jacobi continued fraction expressions, which eventually serve as a key to our determinant evaluations.

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DOI : 10.5802/crmath.569
Classification : 11B68, 11C20, 30B70, 33D45

Chern, Shane  1   ; Jiu, Lin  2

1 Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, B3H 4R2, Canada
2 Zu Chongzhi Center for Mathematics and Computational Sciences, Duke Kunshan University, Kunshan, Suzhou, Jiangsu Province, 215316, PR China
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {Hankel determinants and {Jacobi} continued fractions for $q${-Euler} numbers},
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Chern, Shane; Jiu, Lin. Hankel determinants and Jacobi continued fractions for $q$-Euler numbers. Comptes Rendus. Mathématique, Tome 362 (2024) no. G2, pp. 203-216. doi: 10.5802/crmath.569

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