New inequalities of Huygens-type involving tangent and sine functions

Authors : Ling ZHU, Branko MALESEVİC

Pages : 36-61

Doi:10.15672/hujms.951700

View : 12 | Download : 6

Publication Date : 2023-02-15

Article Type : Research Paper

Abstract :Using the estimations of the even-indexed Bernoulli number and Euler number this paper established some new inequalities for the three functions $2\\leftinsert ignore into journalissuearticles values( \\sin x\\right); /x+\\leftinsert ignore into journalissuearticles values( \\tan x\\right); /x$, $\\leftinsert ignore into journalissuearticles values( \\sin x\\right); /x+2\\leftinsert ignore into journalissuearticles values( \\tan insert ignore into journalissuearticles values(x/2);\\right); /\\leftinsert ignore into journalissuearticles values( 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