Comptes Rendus
Article de recherche - Théorie des nombres
Hankel determinants and Jacobi continued fractions for q-Euler numbers
Shane Chern1  ; Lin Jiu2
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
Comptes Rendus. Mathématique, Volume 362 (2024), 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
Shane Chern 1 ; Lin Jiu 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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Shane Chern; Lin Jiu. Hankel determinants and Jacobi continued fractions for $q$-Euler numbers. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 203-216. doi : 10.5802/crmath.569. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.569/

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