Monotonic and Logarithmically Convex Properties of a Function Involving Gamma Functions
Journal of Inequalities and Applications, 2009 Using the series-expansion of digamma functions and other techniques, some monotonicity and logarithmical concavity involving the ratio of gamma function are obtained, which is to give a partially affirmative answer to an open problem posed by B.-N.Guo ...
Tie-Hong Zhao +2 more
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Extension of complete monotonicity results involving the digamma function
Moroccan Journal of Pure and Applied Analysis, 2018 By using some analytical techniques, we prove a complete monotonicity property of a certain function involving the (p, k)-digamma function. Subsequently, we derive some inequalities for the (p, k)- digamma function.
Nantomah Kwara
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The sum of the series of reciprocals of the cubic polynomials with one zero and double non-zero integer root [PDF]
Mathematics in Education, Research and Applications, 2019 This contribution is a follow-up to author’s previous published papers and deals with the sum of the series of reciprocals of the cubic polynomials with one zero and double non-zero integer root.
Radovan Potůček
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On special Riemann xi function formulae of Hardy involving the digamma function [PDF]
, 2021 We consider some properties of integrals considered by Hardy and Koshliakov that have connections to the digamma function. We establish a new general integral formula that provides a connection to the polygamma function.
Patkowski Alexander E.
core
MONOTONICITY AND CONVEXITY PROPERTIES OF THE NIELSEN’S β-FUNCTION
Проблемы анализа, 2017 The Nielsen’s β-function provides a powerful tool for evaluating and estimating certain integrals, series and mathematical constants. It is related to other special functions such as the digamma function, the Euler’s beta function and the Gauss ...
Kwara Nantomah
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On the positivity of a certain function related with the Digamma function
The Ramanujan Journal, 2023 Abstract In this note, we prove that $$\begin{aligned} \left( \frac{x^n}{1-e^{-x}}\right) ^{(n)}>0 \end{aligned}$$
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Complete monotonicity related to the k-polygamma functions with applications
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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Complete monotonicity of some functions involving k-digamma function with application [PDF]
Journal of Mathematical Inequalities, 2021 Summary: We present several complete monotonicity properties involving \(k\)-digamma function with single parameter. These established results provide a \(k\)-generalization for the known results obtained by \textit{T. Burić} and \textit{N. Elezović}, J. Math. Inequal. 9, No. 4, 1181--1190 (2015; Zbl 1333.26034).
Yin, Li, Huang, Li-Guo, Lin, Xiu-Li
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Hermite-Hadamard-Type Integral Inequalities for Convex Functions and Their Applications
Mathematics, 2022 In this paper, we establish new generalizations of the Hermite-Hadamard-type inequalities. These inequalities are formulated in terms of modules of certain powers of proper functions. Generalizations for convex functions are also considered.
Hari M. Srivastava +2 more
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Computation of the Gamma, Digamma, and Trigamma Functions [PDF]
SIAM Journal on Numerical Analysis, 1994 This paper gives an approximation for gamma function that, while different, has the same form as Lanczos one. Both approximations correct Stirling's approximation with contributions from the gamma function's poles a require \(O (-\log \varepsilon)\) time independent of \(z\) to calculate \(z!\) with \(a\) relative error \(\varepsilon\).
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