An Approximation Formula for Nielsen’s Beta Function Involving the Trigamma Function
Mathematics, 2022 We prove that the function σ(s) defined by β(s)=6s2+12s+53s2(2s+3)−ψ′(s)2−σ(s)2s5,s>0, is strictly increasing with the sharp bounds ...
Mansour Mahmoud, Hanan Almuashi
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Decreasing and complete monotonicity of functions defined by derivatives of completely monotonic function involving trigamma function [PDF]
Demonstratio MathematicaIn this study, using convolution theorem of the Laplace transforms, a monotonicity rule for the ratio of two Laplace transforms, Bernstein’s theorem for completely monotonic functions, and other analytic techniques, the authors verify decreasing property
Yin Hong-Ping, Han Ling-Xiong, Qi Feng
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A Double Inequality for the Trigamma Function and Its Applications [PDF]
Abstract and Applied Analysis, 2014 We prove that p=1 and q=2 are the best possible parameters in the interval (0,∞) such that the double inequality ep/x+1-e-p/x ...
Zhen-Hang Yang +2 more
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Bounds for completely monotonic degree of a remainder for an asymptotic expansion of the trigamma function [PDF]
Arab Journal of Basic and Applied Sciences, 2021 In the paper, the author presents bounds for completely monotonic degree of a remainder for an asymptotic expansion of the trigamma function. This result partially confirms one in a series of conjectures on completely monotonic degrees of remainders of ...
Feng Qi
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Qi’s conjectures on completely monotonic degrees of remainders of asymptotic formulas of di- and trigamma functions [PDF]
Journal of Inequalities and Applications, 2020 Several conjectures posed by Qi on completely monotonic degrees of remainders for the asymptotic formulas of the digamma and trigamma functions are proved.
Ai-Min Xu, Zhong-Di Cen
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Complete Monotonicity of a Difference Between the Exponential and Trigamma Functions and Properties Related to a Modified Bessel Function [PDF]
Mediterranean Journal of Mathematics, 2013 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Feng Qi, Christian Berg
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Some Inequalities for the Trigamma Function in Terms of the Digamma Function [PDF]
Applied Mathematics and Computation, 2015 In the paper, the authors establish three kinds of double inequalities for the trigamma function in terms of the exponential function to powers of the digamma function. These newly established inequalities extend some known results. The method in the paper utilizes some facts from the asymptotic theory and is a natural way to solve problems for ...
Cristinel Mortici, Feng Qi
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Complete Monotonicity of a Difference Between the Exponential and Trigamma Functions
The Pure and Applied Mathematics, 2014 In the paper, by directly verifying an inequality which gives a lower bound for the first order modified Bessel function of the first kind, the authors supply a new proof for the complete monotonicity of a difference between the exponential function $e^{1/t}$ and the trigamma function $ψ'(t)$ on $(0,\infty)$.
Feng Qi
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Three Integral Representations for the Trigamma Function and Some Special Identities [PDF]
Bulletin of Mathematical Sciences and Applications, 2014 We proved three new integral representations for the trigamma function.
Edigles Guedes, K Raja Rama Gandhi
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On the Curvature of the Trigamma Function
Journal of Computational and Applied Mathematics, 1986 Let \(\psi '(x)=d^ 2 \ln \Gamma (x)/dx^ 2\) be the trigamma function. The author proves that \(x\psi\) '(x) is strictly monotonic decreasing for \(x>0\). Two bounds for \(\psi\) '(x) if \(x>0\) are also derived which are sharper than known inequalities. The monotonicity property is relevant in certain fields of statistics. Note that in equation (1.1a),
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