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arXiv · 2102.00388

Evaluations of certain Catalan-Hankel Pfaffians via classical skew orthogonal polynomials

Bo-Jian Shen·Shi-Hao Li·Guo-Fu Yu
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Abstract

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.

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Bo-Jian Shen, Shi-Hao Li, Guo-Fu Yu. 2021-01-31. Evaluations of certain Catalan-Hankel Pfaffians via classical skew orthogonal polynomials. https://doi.org/10.1088/1751-8121/ac0086

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