Orthogonal Polynomials Approach to the Hankel Transform of Sequences Based on Motzkin Numbers

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• 作者：Radica Bojičić…
• 关键词：Hankel transform ; Orthogonal polynomials ; Motzkin numbers
• 刊名：Bulletin of the Malaysian Mathematical Sciences Society
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：40
• 期：1
• 页码：19-33
• 全文大小：
• 刊物类别：Mathematics, general; Applications of Mathematics;
• 刊物主题：Mathematics, general; Applications of Mathematics;
• 出版者：Springer Singapore
• ISSN：2180-4206
• 卷排序：40

文摘

In this paper, we use a method based on orthogonal polynomials to give closed-form evaluations of the Hankel transform of sequences based on the Motzkin numbers. It includes linear combinations of consecutive two, three, and four Motzkin numbers. In some cases, we were able to derive the closed-form evaluation of the Hankel transform, while in the others we showed that the Hankel transform satisfies a particular difference equation. As a corollary, we reobtain known results and show some new results regarding the Hankel transform of Motzkin and shifted Motzkin numbers. Those evaluations also give an idea on how to apply the method based on orthogonal polynomials on the sequences having zero entries in their Hankel transform.