Logarithmic convexity and increasing property of the Bernoulli numbers and their ratios

DOI10.1007/s13398-021-01071-xzbMath1476.11060OpenAlexW3167547514MaRDI QIDQ2050202

Feng Qi, Ye Shuang, Bai-Ni Guo

Publication date: 30 August 2021

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13398-021-01071-x

zbMATH Keywords

Riemann zeta functionintegral representationBernoulli numberStirling number of the second kindcomplete monotonicityratiologarithmic convexityincreasing propertyChebyshev integral inequality

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) (zeta (s)) and (L(s, chi)) (11M06) Inequalities for sums, series and integrals (26D15) Convexity of real functions in one variable, generalizations (26A51) Monotonic functions, generalizations (26A48) Exponential and trigonometric functions (33B10)

Related Items

Increasing property and logarithmic convexity concerning Dirichlet beta function, Euler numbers, and their ratios, Complete monotonicity for a new ratio of finitely many gamma functions, Increasing property and logarithmic convexity of two functions involving Dirichlet eta function, Monotonicity results involving the zeta function with applications, Increasing property and logarithmic convexity of functions involving Dirichlet lambda function, Unnamed Item, Monotonous two-parameter functions for asymptoticly approximating the inequalities involving the inverse tangent functions, On two supercongruences for sums of Apéry-like numbers, Taylor's series expansions for real powers of two functions containing squares of inverse cosine function, closed-form formula for specific partial Bell polynomials, and series representations for real powers of pi, Two identities and closed-form formulas for the Bernoulli numbers in terms of central factorial numbers of the second kind, Bounds for completely monotonic degrees of remainders in asymptotic expansions of the digamma function

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