The ratio monotonicity of the Boros-Moll polynomials

DOI10.1090/S0025-5718-09-02223-6zbMath1221.33036arXiv0806.4333OpenAlexW3104983062MaRDI QIDQ3055199

Ernest X. W. Xia, William Y. C. Chen

Publication date: 7 November 2010

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0806.4333

zbMATH Keywords

Jacobi polynomialsunimodalitylog-concavityBoros-Moll polynomialsratio monotone propertyspiral property

Mathematics Subject Classification ID

Combinatorial inequalities (05A20) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Related Items (17)

A short proof of Moll's minimal conjecture ⋮ Higher order Turán inequalities for Boros-Moll sequences ⋮ A simple proof of higher order Turán inequalities for Boros-Moll sequences ⋮ Refined ratio monotonicity of the coordinator polynomials of the root lattice of type \(B_n\) ⋮ The unimodality of a polynomial coming from a rational integral. Back to the original proof ⋮ \((M,i)\)-multiset Eulerian polynomials ⋮ Properties arising from Laguerre-Pólya class for the Boros-Moll numbers ⋮ Partially 2-colored permutations and the Boros-Moll polynomials ⋮ The concavity and convexity of the Boros-Moll sequences ⋮ 2-Log-Concavity of the Boros–Moll Polynomials ⋮ Nested Log-Concavity ⋮ Skew log-concavity of the Boros-Moll sequences ⋮ On the combinatorics of the Boros-Moll polynomials ⋮ The reverse ultra log-concavity of the Boros-Moll polynomials ⋮ Log-Concavity of Combinations of Sequences and Applications to Genus Distributions ⋮ The greatest lower bound of a Boros-Moll sequence ⋮ A hypergeometric inequality

Cites Work

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• The ratio monotonicity of the \(q\)-derangement numbers
• A formula for a quartic integral: a survey of old proofs and some new ones
• A criterion for unimodality
• An integral hidden in Gradshteyn and Ryzhik
• A sequence of unimodal polynomials
• A Computer Proof of Moll’s Log-Concavity Conjecture
• The double square root, Jacobi polynomials and Ramanujan's master theorem
• An extension of a criterion for unimodality

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