论文标题
加泰罗尼亚数字和雅各比多项式
Catalan Numbers and Jacobi Polynomials
论文作者
论文摘要
我们证明，加泰罗尼亚数字的互换的Hankel矩阵的倒数具有整数条目。我们将结果推广到无限的加泰罗尼亚州数字。我们认为的Hankel矩阵与Jacobi多项式变体的正交多项式有关。我们的证明使用基于Wilf-Zeilberger理论的这些多项式和计算机代数。
We prove that the inverse of the Hankel matrix of the reciprocals of the Catalan numbers has integer entries. We generalize the result to an infinite family of generalized Catalan numbers. The Hankel matrices that we consider are associated with orthogonal polynomials that are variants of Jacobi polynomials. Our proofs use these polynomials and computer algebra based on Wilf-Zeilberger theory.
