Hankel Determinants of a Linear Combination of Three Successive Catalan Numbers

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• 作者：Belgacem Bouras (1)
  
• 关键词：Primary 33C45 ; Secondary 42C05 ; Hankel determinants ; Catalan numbers ; Jacobi polynomials ; Recurrence coefficients ; Linear functional
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2013
• 出版时间：May 2013
• 年：2013
• 卷：10
• 期：2
• 页码：693-705
• 全文大小：260KB
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• 作者单位：Belgacem Bouras (1)
  
  1. Department of Mathematics, Faculty of Science of Gabes, District Riyadh鈥揨rig, Gabes, 6072, Tunisia
  
• ISSN：1660-5454

文摘

We evaluate the determinants of Hankel matrices, whose elements are a linear combination of three successive shifted Catalan numbers. This is done by finding a Jacobi linear functional, such that their moments are, up to a multiplicative constant, the Catalan numbers. The values of such determinants are then expressed in terms of Jacobi polynomials.