论文标题
超夫夫人和塞尔伯格积分的次要求和公式
Minor summation formula of hyperpfaffians and Selberg integrals
论文作者
论文摘要
在上一篇论文中（J.Combin。理论Ser。A，120，2013，1263--1284）H。Tagawa和两位作者提出了一种代数方法来计算某些与与经典正交多核的矩序列相关的hankel决定因素的PFAFFIAN。在论文的最后，他们提供了几种猜想。在这项工作中，我们采用了一种完全不同的方法来评估这种类型的Pfaffians。这个想法是应用某些de bruijn类型公式，并将Pfaffians的评估转换为某些Selberg型积分。这种方法不仅适用于Pfaffians，还适用于Hyperpfaffians。因此，它使我们能够建立比上一篇论文中猜想的身份更广泛的身份。我们还研究了一些与古典$ Q $ - 正交多项式有关的PFAFFIAN。
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 certain Pfaffians whose form resemble to Hankel determinants associated with moment sequences of the classical orthogonal polynomials. At the end of the paper they offered several conjectures. In this work we employ a completely different method to evaluate this type of Pfaffians. The idea is to apply certain de Bruijn type formula and convert the evaluation of the Pfaffians to the certain Selberg type integrals. This approach works not only for Pfaffians but also for hyperpfaffians. Hence it enables us to establish much more generalized identities than those conjectured in the previous paper. We also investigate some Pfaffians related to classical $q$-orthogonal polynomials.
