The -analogs of Bernoulli and Euler numbers were introduced by Carlitz in 1948. Similar to recent results on the Hankel determinants for the -Bernoulli numbers established by Chapoton and Zeng, we perform a parallel analysis for the -Euler numbers. It is shown that the associated orthogonal polynomials for -Euler numbers are given by a specialization of the big -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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