Results 21 to 30 of about 5,395,506 (201)
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 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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On a Conjecture of Alzer, Berg, and Koumandos
Mathematics, 2020 In this paper, we find a solution of an open problem posed by Alzer, Berg, and Koumandos: determine ( α , m ) ∈ R + × N such that the function x α | ψ ( m ) ( x ) | is completely monotonic on ( 0 , ∞ ) , where ψ (
Ladislav Matejíčka
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An inequality involving the gamma and digamma functions [PDF]
Journal of Applied Analysis, 2016 Abstract In the paper, the authors establish an inequality involving the gamma and digamma functions and apply it to prove the negativity and monotonicity of a function involving the gamma and digamma functions.
Qi, Feng, Guo, Bai-Ni
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General infinite series evaluations involving Fibonacci numbers and the Riemann zeta function
Математичні Студії, 2021 The purpose of this paper is to present closed forms for various types of infinite series involving Fibonacci (Lucas) numbers and the Riemann zeta function at integer arguments.
R. Frontczak, T. Goy
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Some exponential and trigonometric integrals involving the log gamma function [PDF]
, 2022 This paper considers some integrals where the integrand comprises the log gamma function or the digamma function multiplied by exponential or trigonometric ...
Connon, Donal F.
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Some series whose coefficients involve the value ζ(n) for $n$n odd
International Journal of Mathematics and Mathematical Sciences, 1989 By using two basic formulas for the digamma function, we derive a variety of series that involve as coefficients the values (2n+1), n=1,2,⋯, of the Riemann-zeta function.
L. R. Bragg
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Sharp bounds for a ratio of the q-gamma function in terms of the q-digamma function
Journal of Inequalities and Applications, 2021 In the present paper, we introduce sharp upper and lower bounds to the ratio of two q-gamma functions Γ q ( x + 1 ) / Γ q ( x + s ) ${\Gamma }_{q}(x+1)/{\Gamma }_{q}(x+s)$ for all real number s and 0 < q ≠ 1 $0< q\neq1$ in terms of the q-digamma function.
Faris Alzahrani +2 more
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Pole decomposition of BFKL eigenvalue at zero conformal spin and the real part of digamma function
Physics Letters BWe consider the powers of leading order eigenvalue of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) equation at zero conformal spin. Using reflection identities of harmonic sums we demonstrate how involved generalized polygamma functions are introduced by ...
Mohammad Joubat +2 more
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, 2016 If the 750 GeV resonance in the diphoton channel is confirmed, what are the measurements necessary to infer the properties of the new particle and understand its nature?
Jernej F. Kamenik +19 more
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