This paper is to evaluate certain Catalan-Hankel Pfaffians by the theory of skew orthogonal polynomials. Due to different kinds of hypergeometric orthogonal polynomials underlying the Askey scheme, we explicitly construct the classical skew orthogonal polynomials and then give different examples of Catalan-Hankel Pfaffians with continuous and q-moment sequences.

中文翻译：

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通过经典偏斜正交多项式评估某些 Catalan-Hankel Pfaffians

本文旨在通过偏斜正交多项式理论来评估某些 Catalan-Hankel Pfaffians。由于 Askey 方案中存在不同种类的超几何正交多项式，我们明确地构造了经典偏斜正交多项式，然后给出了具有连续和q矩序列的 Catalan-Hankel Pfaffians 的不同例子。