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2018 The real-rootedness of generalized Narayana polynomials related to the Boros-Moll polynomials
Herman Z.Q. Chen, Arthur L.B. Yang, Philip B. Zhang
Rocky Mountain J. Math. 48(1): 107-119 (2018). DOI: 10.1216/RMJ-2018-48-1-107

Abstract

In this paper, we prove the real-rootedness of a family of generalized Narayana polynomials which arose in the study of the infinite log-concavity of the Boros-Moll polynomials. We establish certain recurrence relations for these Narayana polynomials, from which we derive the real-rootedness. In order to prove the real-rootedness, we use a sufficient condition due to Liu and Wang to determine whether two polynomials have interlaced zeros. The recurrence relations are verified with the help of the $Mathematica$ package $HolonomicFunctions$.

Citation

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Herman Z.Q. Chen. Arthur L.B. Yang. Philip B. Zhang. "The real-rootedness of generalized Narayana polynomials related to the Boros-Moll polynomials." Rocky Mountain J. Math. 48 (1) 107 - 119, 2018. https://doi.org/10.1216/RMJ-2018-48-1-107

Information

Published: 2018
First available in Project Euclid: 28 April 2018

zbMATH: 1385.05014
MathSciNet: MR3795735
Digital Object Identifier: 10.1216/RMJ-2018-48-1-107

Subjects:
Primary: 05A15, 26C10

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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