On normalized tails of series expansion of generating function of Bernoulli numbers

DOI10.1090/proc/16877MaRDI QIDQ6654028

Gui Zhi Zhang, Feng Qi, Zhen-Hang Yang

Publication date: 18 December 2024

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

zbMATH Keywords

integral representationseries expansionpositivitygenerating functioninequalityBernoulli numberBernoulli polynomialratiodecreasing propertynormalized tail

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Bernoulli and Euler numbers and polynomials (11B68) Convexity of real functions in one variable, generalizations (26A51) Monotonic functions, generalizations (26A48) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Remainders in approximation formulas (41A80)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Approximations for certain hyperbolic functions by partial sums of their Taylor series and completely monotonic functions related to gamma function
• On the log-concavity of the fractional integral of the sine function
• Remarks on some completely monotonic functions
• Properties and applications of a function involving exponential functions
• A double inequality for the ratio of two non-zero neighbouring Bernoulli numbers
• A ratio of finitely many gamma functions and its properties with applications
• Logarithmic convexity and increasing property of the Bernoulli numbers and their ratios
• Decreasing properties of two ratios defined by three and four polygamma functions
• Two identities and closed-form formulas for the Bernoulli numbers in terms of central factorial numbers of the second kind
• Monotonicity criterion for the quotient of power series with applications
• The best bounds in Gautschi-Kershaw inequalities
• Closed-form formulas, determinantal expressions, recursive relations, power series, and special values of several functions used in Clark--Ismail's two conjectures
• A series expansion of a logarithmic expression and a decreasing property of the ratio of two logarithmic expressions containing cosine

Related Items (1)

On convexity and power series expansion for logarithm of normalized tail of power series expansion for square of tangent

This page was built for publication: On normalized tails of series expansion of generating function of Bernoulli numbers