Closed-form expression for Hankel determinants of the Narayana polynomials

Marko D. Petković; Paul Barry; Predrag Rajković

Czechoslovak Mathematical Journal (2012)

  • Volume: 62, Issue: 1, page 39-57
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Petković, Marko D., Barry, Paul, and Rajković, Predrag. "Closed-form expression for Hankel determinants of the Narayana polynomials." Czechoslovak Mathematical Journal 62.1 (2012): 39-57. <http://eudml.org/doc/246667>.

@article{Petković2012,
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.},
author = {Petković, Marko D., Barry, Paul, Rajković, Predrag},
journal = {Czechoslovak Mathematical Journal},
keywords = {Narayana numbers; Hankel transform; orthogonal polynomials; Narayana numbers; Hankel transform; orthogonal polynomials},
language = {eng},
number = {1},
pages = {39-57},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Closed-form expression for Hankel determinants of the Narayana polynomials},
url = {http://eudml.org/doc/246667},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Petković, Marko D.
AU - Barry, Paul
AU - Rajković, Predrag
TI - Closed-form expression for Hankel determinants of the Narayana polynomials
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 1
SP - 39
EP - 57
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.
LA - eng
KW - Narayana numbers; Hankel transform; orthogonal polynomials; Narayana numbers; Hankel transform; orthogonal polynomials
UR - http://eudml.org/doc/246667
ER -

References

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