Hankel transforms of generalized Motzkin numbers |
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| Authors: | Radica Bojičić Marko D. Petković Predrag M. Rajković |
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| Affiliation: | 1. Faculty of Economy, University of Kosovska Mitrovica, Kosovska Mitrovica, Serbia;2. Faculty of Sciences and Mathematics, University of Ni?, Ni?, Serbia;3. Faculty of Mechanical Engineering, University of Ni?, Ni?, Serbia |
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| Abstract: | We study Hankel transform of the sequences (u,l,d),t, and the classical Motzkin numbers. Using the method based on orthogonal polynomials, we give closed‐form evaluations of the Hankel transform of the aforementioned sequences, sums of two consecutive, and shifted sequences. We also show that these sequences satisfy some interesting convolutional properties. Finally, we partially consider the Hankel transform evaluation of the sums of two consecutive shifted (u,l,d)‐Motzkin numbers. Copyright © 2017 John Wiley & Sons, Ltd. |
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| Keywords: | Motzkin numbers t‐Motzkin numbers (u l d)‐Motzkin numbers Hankel transform orthogonal polynomials |
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