Turán type inequalities for the partial sums of the generating functions of Bernoulli and Euler numbers

DOI10.1002/mana.201100299zbMath1272.11038OpenAlexW2071154394MaRDI QIDQ4902785

Stamatis Koumandos, Henrik Laurberg Pedersen

Publication date: 17 January 2013

Published in: Mathematische Nachrichten (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mana.201100299

zbMATH Keywords

generating functionsBernoulli numbers\(\beta\)-functionEuler numberscompletely monotonic functions of positive orderTuran inequalityratio of series of functionsremainders in asymptotic expansions

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Inequalities for sums, series and integrals (26D15) Special sequences and polynomials (11B83) Remainders in approximation formulas (41A80) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20) Inequalities involving other types of functions (26D07)

Related Items (7)

Hypergeometric Euler numbers ⋮ Combinatorial aspects of poly-Bernoulli polynomials and poly-Euler numbers ⋮ Complementary Euler numbers ⋮ Turán-Type Inequalities for Some Lommel Functions of the First Kind ⋮ Monotonicity properties related to the ratio of two gamma functions ⋮ On the log-concavity of the fractional integral of the sine function ⋮ On asymptotic expansions of generalized Stieltjes functions

Cites Work

• Unnamed Item
• Sharp Turán inequalities via very hyperbolic polynomials
• Turán inequalities for three-term recurrences with monotonic coefficients
• Remarks on some completely monotonic functions
• Turán type inequalities for generalized complete elliptic integrals
• Moment inequalities and the Riemann hypothesis
• Completely monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function
• Bounds on Turán determinants
• A lower bound for orthogonal polynomials with an application to polynomial hypergroups
• Some inequalities for Bernoulli's polynomials and related functions
• On some Turán-type inequalities
• On certain determinants whose elements are orthogonal polynomials
• Error Bounds for Asymptotic Expansions of the Ratio of Two Gamma Functions
• Higher order Turán inequalities for the Riemann $\xi$-function
• COMPLETELY MONOTONIC FUNCTIONS RELATED TO LOGARITHMIC DERIVATIVES OF ENTIRE FUNCTIONS
• On the asymptotic expansion of the logarithm of Barnes triple gamma function
• On the Composition of Completely Monotonic Functions and Completely Monotonic Sequences and Related Questions
• Special Functions, Stieltjes Transforms and Infinite Divisibility
• Higher order Turán inequalities
• TURÁN TYPE INEQUALITIES FOR MODIFIED BESSEL FUNCTIONS
• On an inequality of P. Turán concerning Legendre polynomials
• On inequalities of the Turán type
• What is the Laplace Transform?
• Conjectures and theorems in the theory of entire functions

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