Results 1 to 10 of about 99 (89)
Some inequalities involving the polygamma functions [PDF]
Journal of Inequalities and Applications, 2019 Let ψn(x)=(−1)n−1ψ(n)(x) $\psi _{n}(x)=(-1)^{n-1}\psi ^{(n)}(x)$, where ψ(n)(x) $\psi ^{(n)}(x)$ are the polygamma functions. We determine necessary and sufficient conditions for the monotonicity and convexity of the function F(x;α,β)=ln(exp(αψ(x+β))ψn(x)
Lichun Liang, Bin Zhao, Aibing Li
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Sharp Inequalities for Polygamma Functions [PDF]
Mathematica Slovaca, 2015 Abstract In the paper, the authors review some inequalities and the (logarithmically) complete monotonicity concerning the gamma and polygamma functions and, more importantly, present a sharp double inequality for bounding the polygamma function by rational functions.
Bai-Ni Guo, Feng Qi, Qiu-Ming Luo
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Complete monotonicity related to the k-polygamma functions with applications [PDF]
Advances in Difference Equations, 2019 In this paper, we prove complete monotonicity of some functions involving k-polygamma functions. As an application of the main result, we also give new upper and lower bounds of the k-digamma function.
Li Yin, Jumei Zhang, XiuLi Lin
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A Generalized Polygamma Function
Integral Transforms and Special Functions, 2004 14 ...
Victor Moll
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Some completely monotonic functions involving the polygamma functions [PDF]
Journal of Inequalities and Applications, 2019 Motivated by existing results, we present some completely monotonic functions involving the polygamma functions.
Peng Gao
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Polygamma Functions of Negative Order
Journal of Computational and Applied Mathematics, 1998 Liouville's fractional integration is used to define polygamma functions ψ(n)(Z) for negative integer n. It is shown that such ψ(n)(Z) can be represented in a closed form by means of the first derivatives of the Hurwitz Zeta function. Relations to the Barnes G-function and generalized Glaisher's constants are also discussed.
exaly +2 more sources
On Some Properties of Digamma and Polygamma Functions
Journal of Mathematical Analysis and Applications, 2007 The author proves some interesting inequalities involving the logarithmic derivative of the gamma function \(\psi(x)=\frac{\Gamma^{\prime}(x)}{\Gamma(x)}\), and its derivatives \(\psi_{n}(x)=\psi^{(n)}(x),\;n=1,2,3,\ldots\), known as polygamma functions.
Necdet Batir
exaly +3 more sources
Turán-Type Inequalities for Generalized Polygamma Function
International Journal of Scientific Research in Science and Technology, 2022 Inspired by the work of C. Mortici [1] and A. Laforgia et. al [2] we have established some new Turán-type inequalities for k-polygamma function and p-k-polygamma function.
exaly +4 more sources
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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On the Hurwitz zeta function with an application to the beta-exponential distribution
Journal of Inequalities and Applications, 2020 We prove a monotonicity property of the Hurwitz zeta function which, in turn, translates into a chain of inequalities for polygamma functions of different orders.
Julyan Arbel +2 more
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