The 2-log-convexity of the Apéry Numbers

DOI10.1090/S0002-9939-2010-10575-0zbMath1290.05025arXiv0912.0795OpenAlexW2963369124MaRDI QIDQ3082308

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

Publication date: 10 March 2011

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.0795

zbMATH Keywords

log-convexityApéry number2-log-convexityinfinite log-convexity

Mathematics Subject Classification ID

Combinatorial inequalities (05A20) Recurrences (11B37) Special sequences and polynomials (11B83)

Related Items (17)

Hamburger moment sequences in combinatorics ⋮ Proof of a conjecture of Z.-W. Sun on ratio monotonicity ⋮ The ratio log-concavity of the Cohen numbers ⋮ Two-Motzkin-like numbers and Stieltjes moment sequences ⋮ Positivity of Iterated Sequences of Polynomials ⋮ Infinitely log-monotonic combinatorial sequences ⋮ A criterion for the log-convexity of combinatorial sequences ⋮ The asymptotic log-convexity of Apéry-like numbers ⋮ Two-log-convexity of the Catalan-Larcombe-French sequence ⋮ Asymptotic \(r\)-log-convexity and P-recursive sequences ⋮ \(r\)-log-concavity of partition functions ⋮ Apéry polynomials and the multivariate saddle point method ⋮ The Euler and Springer numbers as moment sequences ⋮ Log-behavior of two sequences related to the elliptic integrals ⋮ Log-convex and Stieltjes moment sequences ⋮ Hankel-total positivity of some sequences ⋮ Proof of a conjecture of Z.W. Sun

Uses Software

• SumTools

Cites Work

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• An algorithmic proof theory for hypergeometric (ordinary and ``\(q\)) multisum/integral identities
• Some congruences for the Apéry numbers
• Congruence properties of Apéry numbers
• Some congruences for Apery numbers
• A binomial coefficient identity associated to a conjecture of Beukers
• Recurrences and Legendre transform
• Another congruence for the Apéry numbers
• An Apéry-like difference equation for Catalan's constant
• Binomial sums related to rational approximations to \(\zeta(4)\)
• Logarithmic behavior of some combinatorial sequences
• Log-balanced combinatorial sequences
• Hypergéométrie et fonction zêta de Riemann

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