A direct method for evaluating some nice Hankel determinants and proofs of several conjectures

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• 作者：Xiang-Ke Chang^a ; ^b ; ^{changxk@lsec.cc.ac.cn} ; Xing-Biao Hu^a ; ^{hxb@lsec.cc.ac.cn} ; Ying-Nan Zhang^a ; ^b ; ^{zhangyingnan@lsec.cc.ac.cn}
• 关键词：05A15 ; 11B83 ; 15A15
• 刊名：Linear Algebra and its Applications
• 出版年：2013
• 出版时间：1 March, 2013
• 年：2013
• 卷：438
• 期：5
• 页码：2523-2541
• 全文大小：333 K

文摘

In this paper, we propose a direct method to evaluate Hankel determinants for some generating functions satisfying a certain type of quadratic equations, which cover generating functions of Catalan numbers, Motzkin numbers and Schr?der numbers. Additionally, four recent conjectures proposed by Cigler (2011) are proved.