Results 1 to 10 of about 265 (93)
Increasing property and logarithmic convexity of functions involving Dirichlet lambda function
Demonstratio Mathematica, 2023 In this article, with the help of an integral representation of the Dirichlet lambda function, by means of a monotonicity rule for the ratio of two integrals with a parameter, and by virtue of complete monotonicity and another property of an elementary ...
Qi Feng, Lim Dongkyu
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Demonstratio Mathematica, 2022 In this article, the authors present two identities involving products of the Bernoulli numbers, provide four alternative proofs for these two identities, derive two closed-form formulas for the Bernoulli numbers in terms of central factorial numbers of ...
Chen Xue-Yan +3 more
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On logarithm of circular and hyperbolic functions and bounds for exp(±x2)
Acta Universitatis Sapientiae: Mathematica, 2022 We show that certain known or new inequalities for the logarithm of circular hyperbolic functions imply bounds for exp(±x2) proved in [1].
Sándor József
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Learning linear non-Gaussian graphical models with multidirected edges
Journal of Causal Inference, 2021 In this article, we propose a new method to learn the underlying acyclic mixed graph of a linear non-Gaussian structural equation model with given observational data.
Liu Yiheng, Robeva Elina, Wang Huanqing
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On the generalized Becker-Stark type inequalities
Acta Universitatis Sapientiae: Mathematica, 2021 In this paper, we establish several generalized Becker-Stark type inequalities for the tangent function. We present unified proofs of many inequalities in the existing literature. Graphical illustrations of some obtained results are also presented.
Bagul Yogesh J. +3 more
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Several explicit formulas for (degenerate) Narumi and Cauchy polynomials and numbers
Open Mathematics, 2021 In this paper, with the aid of the Faà di Bruno formula and by virtue of properties of the Bell polynomials of the second kind, the authors define a kind of notion of degenerate Narumi numbers and polynomials, establish explicit formulas for degenerate ...
Qi Feng +2 more
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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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Binet's second formula, Hermite's generalization, and two related identities
Open Mathematics, 2023 Legendre was the first to evaluate two well-known integrals involving sines and exponentials. One of these integrals can be used to prove Binet’s second formula for the logarithm of the gamma function.
Boyack Rufus
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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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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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