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Evaluations of certain Catalan-Hankel Pfaffians via classical skew orthogonal polynomials
Published 31 Jan 2021 in math.CA, math-ph, and math.MP | (2102.00388v1)
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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