An infinite sequence of inequalities involving special values of the Riemann zeta function

DOI10.7153/mia-2018-21-02zbMath1401.11122OpenAlexW2766444644MaRDI QIDQ4606361

Mircea Merca

Publication date: 2 March 2018

Published in: Mathematical Inequalities & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.7153/mia-2018-21-02

zbMATH Keywords

Riemann zeta functionsymmetric functionsChebyshev-Stirling numbers of the first kind

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) (zeta (s)) and (L(s, chi)) (11M06) Inequalities for sums, series and integrals (26D15)

Related Items (4)

Monotonicities of some functions involving multiple logarithm function and their applications ⋮ A note on the positivity of the even degree complete homogeneous symmetric polynomials ⋮ Euler-Riemann zeta function and Chebyshev-Stirling numbers of the first kind ⋮ New bounds for the ratio of two adjacent even-indexed Bernoulli numbers

Cites Work

• A convolution for complete and elementary symmetric functions
• Total positivity properties of Jacobi-Stirling numbers
• Combinatorial interpretations of particular evaluations of complete and elementary symmetric functions
• Jacobi-Stirling polynomials and \(P\)-partitions
• The continuing story of zeta
• The cardinal sine function and the Chebyshev-Stirling numbers
• Combinatorial interpretations of the Jacobi-Stirling numbers
• The Jacobi-Stirling numbers
• A connection between Jacobi-Stirling numbers and Bernoulli polynomials
• The Legendre-Stirling numbers
• On the asymptotic normality of the Legendre-Stirling numbers of the second kind
• Jacobi-Stirling numbers, Jacobi polynomials, and the left-definite analysis of the classical Jacobi differential expression
• Asymptotics of the Chebyshev–Stirling numbers of the first kind
• A note on the Jacobi–Stirling numbers
• Asymptotics of Stirling and Chebyshev-Stirling Numbers of the Second Kind
• Elementary Evaluation of ζ(2n)
• A combinatorial interpretation of the Legendre-Stirling numbers
• New convolutions for complete and elementary symmetric functions
• A simple derivation of \(\zeta(1-K)=-B_K/K\).
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