More Jordan type inequalities

D. Aharonov; U. Elias

doi:10.7153/mia-17-115

More Jordan type inequalities

D. Aharonov, U. Elias

Research output: Contribution to journal › Article › peer-review

Abstract

The function tan(πx/2)/(πx/2) is expanded into a Laurent series of 1 - x², where the coefficients are given explicitly as combinations of zeta function of even integers. This is used to achieve a sequence of upper and lower bounds which are very precise even at the poles at x = ±1. Similar results are obtained for other trigonometric functions with poles.

Original language	English
Pages (from-to)	1563-1577
Number of pages	15
Journal	Mathematical Inequalities and Applications
Volume	17
Issue number	4
DOIs	https://doi.org/10.7153/mia-17-115
State	Published - 1 Oct 2014

Keywords

Dirichlet functions
Jordan inequality
Laurent series
Trigonometric inequalities
Zeta function

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.7153/mia-17-115

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More Jordan type inequalities

Abstract

Keywords

ASJC Scopus subject areas

UN SDGs

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