Monotonicity and absolute monotonicity for the two-parameter hyperbolic and trigonometric functions with applications

DOI10.1186/s13660-016-1143-8zbMath1346.33001OpenAlexW2507371854WikidataQ59466616 ScholiaQ59466616MaRDI QIDQ308172

Zhen-Hang Yang, Yu-Ming Chu

Publication date: 5 September 2016

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13660-016-1143-8

zbMATH Keywords

error functiongamma functiontrigonometric functionStolarsky meancomplete monotonicityhyperbolic functionabsolute monotonicity

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Monotonic functions, generalizations (26A48) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20) Inequalities involving other types of functions (26D07) Exponential and trigonometric functions (33B10)

Related Items

Complete monotonicity involving some ratios of gamma functions ⋮ Logarithmically absolutely monotone trigonometric functions ⋮ A comparison theorem for two divided differences and applications to special functions ⋮ Some properties of the divided difference of psi and polygamma functions ⋮ A class of completely mixed monotonic functions involving the gamma function with applications ⋮ New properties of the divided difference of psi and polygamma functions ⋮ Complete monotonicity and inequalites involving Gurland's ratios of gamma functions ⋮ Logarithmically complete monotonicity of ratios of \(q\)-gamma functions ⋮ Asymptotic expansions for the gamma function in terms of hyperbolic functions ⋮ On complete monotonicity for several classes of functions related to ratios of gamma functions ⋮ Complete monotonicity of the remainder of the asymptotic series for the ratio of two gamma functions

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