34 Result(s)
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Article
Convexity of ratios of the modified Bessel functions of the first kind with applications
Let \(I_{\nu }\left( x\right) \) I ν ...
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Open AccessEditorial Expression of Concern: On approximating Mills ratio
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Article
Open AccessWindschitl type approximation formulas for the gamma function
In this paper, we present four new Windschitl type approximation formulas for the gamma function. By some unique ideas and techniques, we prove that four functions combined with the gamma function and Windschi...
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Article
Open AccessMonotonicity of the ratio of modified Bessel functions of the first kind with applications
Let W v ...
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Open AccessAn accurate approximation formula for gamma function
In this paper, we present a very accurate approximation for the gamma function: Γ ...
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Open AccessSharp Smith’s bounds for the gamma function
Among various approximation formulas for the gamma function, Smith showed that Γ ...
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Open AccessMonotonicity and inequalities for the gamma function
In this paper, by using the monotonicity rule for the ratio of two Laplace transforms, we prove that the function ...
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Article
Open AccessComplete monotonicity involving some ratios of gamma functions
In this paper, by using the properties of an auxiliary function, we mainly present the necessary and sufficient conditions for various ratios constructed by gamma functions to be respectively completely and lo...
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Open AccessOn rational bounds for the gamma function
In the article, we prove that the double inequality ...
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Article
Open AccessMonotonicity rule for the quotient of two functions and its application
In the article, we provide a monotonicity rule for the function [ P ...
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Open AccessSharp inequalities for tangent function with applications
In the article, we present new bounds for the function e ...
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Article
Open AccessOn approximating the modified Bessel function of the second kind
In the article, we prove that the double inequalities ...
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Open AccessNecessary and sufficient conditions for the two parameter generalized Wilker-type inequalities
In the article, we provide the necessary and sufficient conditions for the parameters α and β such that the generalized Wilker-type inequality ...
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Open AccessOn approximating the error function
In the article, we present the necessary and sufficient condition for the parameter p on the interval ...
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Article
Open AccessMonotonicity of the incomplete gamma function with applications
In the article, we discuss the monotonicity properties of the function x ...
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Article
Open AccessMonotonicity and inequalities involving the incomplete gamma function
In the article, we deal with the monotonicity of the function x → ...
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Article
Open AccessMonotonicity of a mean related to polygamma functions with an application
Let ψ n ...
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Article
Open AccessMonotonicity and absolute monotonicity for the two-parameter hyperbolic and trigonometric functions with applications
In this paper, we present the monotonicity and absolute monotonicity properties for the two-parameter hyperbolic and trigonometric functions. As applications, we find several complete monotonicity properties f...
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Article
Open AccessImprovements of the bounds for Ramanujan constant function
In the article, we establish several inequalities for the Ramanujan constant function R ...
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Article
Open AccessGeneralized Wilker-type inequalities with two parameters
In the article, we present certain p , q ...
