Results 71 to 80 of about 2,821,192 (174)

Monotonicity and positivity of several functions involving ratios and products of polygamma functions

Journal of Inequalities and Applications
Let ψ ( x ) $\psi (x)$ denote the digamma function, that is, the logarithmic derivative of the classical Euler gamma function Γ ( x ) $\Gamma (x)$ . In the paper, the authors discover the monotonic properties of the functions ψ ( n ) ( x ) x ψ ( n + 1 ) (
Feng Qi, Dongkyu Lim, Kwara Nantomah
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On the Asymptotic Expansions of the (p,k)-Analogues of the Gamma Function and Associated Functions

Axioms
General asymptotic expansion of the (p,k)-gamma function is obtained and various approaches to this expansion are studied. The numerical precision of the derived asymptotic formulas is shown and compared.
Tomislav Burić
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Complete Monotonicity Properties of a Function Involving the Polygamma Function

Engineering and Applied Science Letters, 2018
In this paper, we study completete monotonicity properties of the function $f_{a,k}(x)=ψ^{(k)}(x+a) - ψ^{(k)}(x) - \frac{ak!}{x^{k+1}}$, where $a\in(0,1)$ and $k\in \mathbb{N}_0$. Specifically, we consider the cases for $k\in \{ 2n: n\in \mathbb{N}_0 \}$ and $k\in \{ 2n+1: n\in \mathbb{N}_0 \}$.
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Inequalities for the polygamma functions with application [PDF]

, 2005
We present some inequalities for the polygamma ...
Chen, Chaoping
core   +1 more source

Families of specialized Euler sums [PDF]

Discrete Mathematics Letters, 2022
Anthony Sofo
doaj   +1 more source

On complete monotonicity for several classes of functions related to ratios of gamma functions

Journal of Inequalities and Applications, 2019
Let Γ(x) $\varGamma (x)$ denote the classical Euler gamma function. The logarithmic derivative ψ(x)=[lnΓ(x)]′=Γ′(x)Γ(x) $\psi (x)=[\ln \varGamma (x)]'=\frac{\varGamma '(x)}{ \varGamma (x)}$, ψ′(x) $\psi '(x)$, and ψ″(x) $\psi ''(x)$ are, respectively ...
Feng Qi, Ravi P. Agarwal
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Probabilistic Multiple-Integral Evaluation of Odd Dirichlet Beta and Even Zeta Functions and Proof of Digamma-Trigamma Reflections

Foundations
The aim of this work was to construct explicit expressions for the summation of Dirichlet Beta functions with odd arguments and Zeta functions with even arguments.
Antonio E. Bargellini, Daniele Ritelli, Giulia Spaletta   +2 more
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An inequality for the q-Polygamma function

Advanced Studies in Theoretical Physics, 2013
An Inequality for the q-Polygamma Function Banyat Sroysang Department of Mathematics and Statistics Faculty of Science and Technology Thammasat University, Pathumthani 12121 Thailand banyat@mathstat.sci.tu.ac.th Copyright c © 2013 Banyat Sroysang. This is an open access article distributed under the Creative Commons Attribution License, which permits ...
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Variant alternating Euler sums of higher order [PDF]

Discrete Mathematics Letters, 2023
Anthony Sofo
doaj   +1 more source

The off-shell one- and two-loop box recovered from intersection theory

Nuclear Physics B
We advertise intersection theory for generalised hypergeometric functions as a means of evaluating Mellin-Barnes representations. As an example, we study two-parameter representations of the off-shell one- and two-loop box graphs in exactly four ...
B. Eden
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