Monotonicity and inequalities for the ratios between two Bernoulli polynomials

2024/05/06 by Zhen-Hang Yang, Feng Qi, Yang, Zhen-Hang +1 · 1 citation
#math.GM

paper · pdf · doi:10.48550/arxiv.2405.05280

Abstract

In the work, the authors establish the monotonicity of the ratios \fracB_2ℓ-1(s)B_2ℓ+1(s), \fracB_2ℓ(s)B_2ℓ+1(s), \fracB_2m(s)B_2ℓ(s), \fracB_2ℓ(s)B_2ℓ-1(s), where B_ℓ(s) denotes the Bernoulli polynomials. From these newly-established monotonicity results, the authors derive some new inequalities and recover several known inequalities of the Bernoulli polynomials B_ℓ(s), the Bernoulli numbers B_2ℓ, and their ratios such as \fracB_2ℓ+2B_2ℓ.

Citations

• Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55)

Cited by

• Theory of Normalized Remainders in Taylor Series Expansions

Related

• On hypergeometric Bernoulli numbers and polynomials
• The Zagier polynomials. Part II: Arithmetic properties of coefficients
• Some results associated with Bernoulli and Euler numbers with applications
• Lecture Notes, Bernoulli Polynomials and Applications
• Ratio Monotonicity of Polynomials Derived from Nondecreasing Sequences