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In the previous paper (J. Combin. Theory Ser. A, 120, 2013, 1263--1284) H.Tagawa and the two authors proposed an algebraic method to compute certainPfaffians whose form resemble to Hankel determinants associated with momentsequences of the classical orthogonal polynomials. At the end of the paper theyoffered several conjectures. In this work we employ a completely differentmethod to evaluate this type of Pfaffians. The idea is to apply certain deBruijn type formula and convert the evaluation of the Pfaffians to the certainSelberg type integrals. This approach works not only for Pfaffians but also forhyperpfaffians. Hence it enables us to establish much more generalizedidentities than those conjectured in the previous paper. We also investigatesome Pfaffians related to classical $q$-orthogonal polynomials.

Minor summation formula of hyperpfaffians and Selberg integrals