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Approximations to inverse tangent function [PDF]

Journal of Inequalities and Applications, 2018
In this paper, we present a sharp Shafer-type inequality for the inverse tangent function. Based on the Padé approximation method, we give approximations to the inverse tangent function. Based on the obtained result, we establish new bounds for arctanx.
Quan-Xi Qiao, Chao-Ping Chen
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Sharp inequalities for tangent function with applications [PDF]

Journal of Inequalities and Applications, 2017
In the article, we present new bounds for the function e t cot ( t ) − 1 $e^{t\cot(t)-1}$ on the interval ( 0 , π / 2 ) $(0, \pi/2)$ and find sharp estimations for the Sine integral and the Catalan constant based on a new monotonicity criterion for the ...
Hui-Lin Lv, Zhen-Hang Yang, Tian-Qi Luo, Shen-Zhou Zheng   +3 more
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Derivatives of tangent function and tangent numbers [PDF]

Applied Mathematics and Computation, 2015
In the paper, by induction, the Fa\`a di Bruno formula, and some techniques in the theory of complex functions, the author finds explicit formulas for higher order derivatives of the tangent and cotangent functions as well as powers of the sine and ...
Bourbaki, Boyadzhiev, Comtet, Daboul, Dominici, Feng Qi, Guo, Guo, Guo, Guo, Guo, Guo, Guo, Guo, Hoffman, Hoffman, Luo, Luo, Ma, Ma, Ma, Qi, Qi, Qi, Qi, Qi, Qi, Qi, Qi, Qi, Qi, Qi, Remmert, Schwatt, Schwatt, Wei, Xu, Zhang   +37 more
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Starlikeness Associated with Tangent Hyperbolic Function

Journal of Function Spaces, 2022
The primary objective of this study is to establish a class of starlike functions (symmetric under rotation) that are related to a tangent hyperbolic.
Huo Tang, Muhammad Arif, Khalil Ullah, Nazar Khan, Mirajul Haq, Bilal Khan   +5 more
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Integrals of hyperbolic tangent function [PDF]

Discrete Mathematics Letters
By means of the contour integration method, we evaluate, in closed form, a class of definite integrals involving hyperbolic tangent function.
Jing Li, Wenchang Chu
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New Bounds for the Sine Function and Tangent Function [PDF]

Mathematics, 2021
Using the power series expansion technique, this paper established two new inequalities for the sine function and tangent function bounded by the functions x2sin(λx)/(λx)α and x2tan(μx)/(μx)β.
Ling Zhu
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Log-tangent integrals and the Riemann zeta function

Mathematical Modelling and Analysis, 2019
We show that integrals involving the log-tangent function, with respect to any square-integrable function on  , can be evaluated by the harmonic series. Consequently, several formulas and algebraic properties of the Riemann zeta function at odd positive ...
Lahoucine Elaissaoui, Zine El-Abidine Guennoun   +1 more
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On Analytic Univalent Function Associated With Tangent Hyperbolic Function [PDF]

Sahand Communications in Mathematical Analysis
Within this article, we propose some sufficient conditions for analytic functions correlated with tangent hyperbolic function. We investigate convolution conditions, integral conservation properties and coefficient sufficiency criteria for this family of
Gehan Elyazyd, Matthew Oluwayemi, Atef Elmahdy, Hanan Darwish   +3 more
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On some determinants involving the tangent function

The Ramanujan Journal, 2019
Let $p$ be an odd prime and let $a,b\in\mathbb Z$ with $p\nmid ab$. In this paper we mainly evaluate $$T_p^{(\delta)}(a,b):=\det\left[\tan\pi\frac{aj^2+bk^2}p\right]_{\delta\le j,k\le (p-1)/2}\ \ (\delta=0,1).$$ For example, in the case $p\equiv3\pmod4 ...
Sun, Zhi-Wei
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A NOTE ON THE BECKER-STARK TYPE INEQUALITIES

Проблемы анализа, 2022
This note is devoted to establishing the sharp bounds for the function 𝑥/ tg 𝑥, thus refining the well-known Becker-Stark’s inequality.
R. M. Dhaigude, Y. J. Bagul
doaj   +1 more source