Results 21 to 30 of about 539 (144)
Refinements of Some Classical Inequalities Involving Sinc and Hyperbolic Sinc Functions
Annales Mathematicae Silesianae, 2023 Several bounds of trigonometric-exponential and hyperbolic-exponential type for sinc and hyperbolic sinc functions are presented. In an attempt to generalize the results, some known inequalities are sharpened and extended.
Bagul Yogesh J. +3 more
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Three families of two-parameter means constructed by trigonometric functions
Journal of Inequalities and Applications, 2013 In this paper, we establish three families of trigonometric functions with two parameters and prove their monotonicity and bivariate log-convexity. Based on them, three two-parameter families of means involving trigonometric functions, which include ...
Zhen-Hang Yang
semanticscholar +2 more sources
Demonstratio Mathematica, 2022 In this article, by virtue of expansions of two finite products of finitely many square sums, with the aid of series expansions of composite functions of (hyperbolic) sine and cosine functions with inverse sine and cosine functions, and in the light of ...
Qi Feng
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Some Inequalities for Generalized Hyperbolic Functions
Moroccan Journal of Pure and Applied Analysis, 2020 In this paper, we establish several inequalities involving certain generalizations of the hyperbolic functions. The established results serve as generalizations of some known results in the literature.
Nantomah Kwara, Prempeh Edward
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Open Mathematics, 2023 In this study, by virtue of a derivative formula for the ratio of two differentiable functions and with aid of a monotonicity rule, the authors expand a logarithmic expression involving the cosine function into the Maclaurin power series in terms of ...
Li Yan-Fang, Qi Feng
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q-Functions and Distributions, Operational and Umbral Methods
Mathematics, 2021 The use of non-standard calculus means have been proven to be extremely powerful for studying old and new properties of special functions and polynomials.
Giuseppe Dattoli +3 more
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An explicit formula for derivative polynomials of the tangent function
Acta Universitatis Sapientiae: Mathematica, 2017 In the paper, the authors derive an explicit formula for derivative polynomials of the tangent function, deduce an explicit formula for tangent numbers, pose an open problem about obtaining an alternative and explicit formula for derivative polynomials ...
Qi Feng, Guo Bai-Ni
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Some properties of the generalized Gaussian ratio and their applications
, 2020 We are devoted to an integral, asymptotic expansion and Maclaurin series representation for the generalized Gaussian ratio, and find their various related properties such as complete monotonicity and some useful inequalities.
Zhen-Hang Yang, B. Xi, Shenzhou Zheng
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A survey for generalized trigonometric and hyperbolic functions
Journal of Mathematical Inequalities, 2019 The generalized trigonometric functions which have a short history, were introduced by Lindqvist two decades ago. Since 2012, many mathematician began to study their classical inequalities, general convexity and concavity, multiple-angle formulas and ...
L. Yin +3 more
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A Series Expansion for Integral Powers of Arctangent [PDF]
Integral Transforms and Special Functions Volume 17, Issue 7, 2006, 2004 A new series expansion for the function (arctan(x)/x)^n is developed and some properties of the expansion coefficients are obtained.
arxiv +1 more source