- Hacettepe Journal of Mathematics and Statistics
- Vol: 52 Issue: 1
- New inequalities of Huygens-type involving tangent and sine functions
New inequalities of Huygens-type involving tangent and sine functions
Authors : Ling Zhu, Branko Malesevic
Pages : 36-61
Doi:10.15672/hujms.951700
View : 12 | Download : 4
Publication Date : 2023-02-15
Article Type : Research
Abstract :Using the estimations of the even-indexed Bernoulli number and Euler number this paper established some new inequalities for the three functions $2\\left( \\sin x\\right) /x+\\left( \\tan x\\right) /x$, $\\left( \\sin x\\right) /x+2\\left( \\tan (x/2)\\right) /\\left( x/2\\right) $ and $2x/\\sin x+x/\\tan x$ bounded by the powers of tangent function.Keywords : circular functions, refinements of the Huygens-type inequalities, even-indexed Bernoulli number, Euler number