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Register a new userHankel hyperpfaffian calculations and Selberg integrals
حسابات هانكل الهايبربفافيان والأستخدامات سيلبيرج
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في الورقة السابقة (J. Combin. Theory Ser. A، 120، 2013، 1263--1284)، قام H. Tagawa والمؤلفين الاثنين باقتراح طريقة جبرية لحساب بعض البفافيان الذين يشبهون التحديدات الهانكل المرتبطة بتسلسلات اللحظات للخطط الهندسية التقليدية. في نهاية الورقة، قدموا عدة افتراضات. في هذا العمل، نستخدم طريقة مختلفة تمامًا لتقدير هذا النوع من البفافيان. فكرة الأمر هي تطبيق صيغة نوع دي بروين وتحويل تقدير البفافيان إلى بعض الأحاديث النوع سيلبرغ. يعمل هذا النهج ليس فقط على البفافيان بل أيضًا على الهايبربفافيان. وبالتالي، يمكنها تأسيس هويات أكثر تطبيقًا بكثير من الأفتراضات التي قدمت في الورقة السابقة. نحاول أيضًا التطبيقات الكوانتومية.
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 attempt q-analogues.
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