Closed-form expression for Hankel determinants of the Narayana polynomials

Marko D. Petković; Paul Barry; Predrag Rajković

doi:10.1007/s10587-012-0015-8

Closed-form expression for Hankel determinants of the Narayana polynomials

Marko D. Petković, Paul Barry, Predrag Rajković

School of Science and Computing

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

We considered a Hankel transform evaluation of Narayana and shifted Narayana polynomials. Those polynomials arises from Narayana numbers and have many combinatorial properties. A mainly used tool for the evaluation is the method based on orthogonal polynomials. Furthermore, we provided a Hankel transform evaluation of the linear combination of two consecutive shifted Narayana polynomials, using the same method (based on orthogonal polynomials) and previously obtained moment representation of Narayana and shifted Narayana polynomials.

Original language	English
Pages (from-to)	39-57
Number of pages	19
Journal	Czechoslovak Mathematical Journal
Volume	62
Issue number	1
DOIs	https://doi.org/10.1007/s10587-012-0015-8
Publication status	Published - Mar 2012

Keywords

Hankel transform
Narayana numbers
orthogonal polynomials

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10.1007/s10587-012-0015-8

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abstract = "We considered a Hankel transform evaluation of Narayana and shifted Narayana polynomials. Those polynomials arises from Narayana numbers and have many combinatorial properties. A mainly used tool for the evaluation is the method based on orthogonal polynomials. Furthermore, we provided a Hankel transform evaluation of the linear combination of two consecutive shifted Narayana polynomials, using the same method (based on orthogonal polynomials) and previously obtained moment representation of Narayana and shifted Narayana polynomials.",

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T1 - Closed-form expression for Hankel determinants of the Narayana polynomials

AU - Petković, Marko D.

AU - Barry, Paul

AU - Rajković, Predrag

PY - 2012/3

Y1 - 2012/3

N2 - We considered a Hankel transform evaluation of Narayana and shifted Narayana polynomials. Those polynomials arises from Narayana numbers and have many combinatorial properties. A mainly used tool for the evaluation is the method based on orthogonal polynomials. Furthermore, we provided a Hankel transform evaluation of the linear combination of two consecutive shifted Narayana polynomials, using the same method (based on orthogonal polynomials) and previously obtained moment representation of Narayana and shifted Narayana polynomials.

AB - We considered a Hankel transform evaluation of Narayana and shifted Narayana polynomials. Those polynomials arises from Narayana numbers and have many combinatorial properties. A mainly used tool for the evaluation is the method based on orthogonal polynomials. Furthermore, we provided a Hankel transform evaluation of the linear combination of two consecutive shifted Narayana polynomials, using the same method (based on orthogonal polynomials) and previously obtained moment representation of Narayana and shifted Narayana polynomials.

KW - Hankel transform

KW - Narayana numbers

KW - orthogonal polynomials

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DO - 10.1007/s10587-012-0015-8

M3 - Article

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SP - 39

EP - 57

JO - Czechoslovak Mathematical Journal

JF - Czechoslovak Mathematical Journal

SN - 0011-4642

IS - 1

ER -

Closed-form expression for Hankel determinants of the Narayana polynomials

Abstract

Keywords

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