Results 31 to 40 of about 519 (71)

A completely monotonic function involving the tri- and tetra-gamma functions

, 2010
The psi function $\psi(x)$ is defined by $\psi(x)=\frac{\Gamma'(x)}{\Gamma(x)}$ and $\psi^{(i)}(x)$ for $i\in\mathbb{N}$ denote the polygamma functions, where $\Gamma(x)$ is the gamma function.
Guo, Bai-Ni, Qi, Feng
core   +1 more source

Some special functions and cylindrical diffusion equation on α-time scale

Demonstratio Mathematica
This article is dedicated to present various concepts on α\alpha -time scale, including power series, Taylor series, binomial series, exponential function, gamma function, and Bessel functions of the first kind.
Silindir Burcu, Tuncer Zehra, Gergün Seçil, Yantir Ahmet   +3 more
doaj   +1 more source

On Solving Some Trigonometric Series [PDF]

, 2013
This communication shows the track for finding a solution for a sin(kx)/k**2 series and a fresh representation for the Euler's Gamma function in terms of Riemann's Zeta function.
Stenlund, Henrik
core  

Sharp bounds for harmonic numbers

, 2010
In the paper, we first survey some results on inequalities for bounding harmonic numbers or Euler-Mascheroni constant, and then we establish a new sharp double inequality for bounding harmonic numbers as follows: For $n\in\mathbb{N}$, the double ...
Alzer, Alzer, Bai-Ni Guo, Batir, Chen, Chen, DeTemple, Feng Qi, Guo, Havil, High, Klambauer, Koumandos, Kuang, Kuang, Kuang, Pólya, Qi, Tóth, Tóth, Wei, Wu, Yang, Young   +23 more
core   +1 more source

Solution to an open problem on a logarithmic integral and derived results

Annals of the West University of Timisoara: Mathematics and Computer Science
This article solves an open problem that was previously stated by providing an exact evaluation of a logarithmic integral. Furthermore, the result is generalized by introducing a new adjustable parameter.
Coine Clément, Chesneau Christophe
doaj   +1 more source

Complete monotonicity of multinomial probabilities and its application to Bernstein estimators on the simplex

, 2018
Let $d\in \mathbb{N}$ and let $\gamma_i\in [0,\infty)$, $x_i\in (0,1)$ be such that $\sum_{i=1}^{d+1} \gamma_i = M\in (0,\infty)$ and $\sum_{i=1}^{d+1} x_i = 1$.
Ouimet, Frédéric
core   +1 more source

Some completely monotonic functions involving the polygamma functions [PDF]

, 2010
Motivated by existing results, we present some completely monotonic functions involving the polygamma functions.Comment: 6 ...
Gao, Peng
core  

On the Power Series Expansion of the Reciprocal Gamma Function [PDF]

, 2017
Using the reflection formula of the Gamma function, we derive a new formula for the Taylor coefficients of the reciprocal Gamma function. The new formula provides effective asymptotic values for the coefficients even for very small values of the indices.
Fekih-Ahmed, Lazhar
core  

A refinement of a double inequality for the gamma function

, 2011
In the paper, we present a monotonicity result of a function involving the gamma function and the logarithmic function, refine a double inequality for the gamma function, and improve some known results for bounding the gamma function.Comment: 8 ...
Guo, Bai-Ni, Qi, Feng
core   +1 more source

The evaluation of a definite integral by the method of brackets illustrating its flexibility

Open Mathematics
The method of brackets is a procedure to evaluate definite integrals over a half-line. It consists of a small number of rules. This article illustrates the method by evaluating an integral by several variations of the method. The integrand is the product
Gonzalez Ivan, Santander John Lopez, Moll Victor H.   +2 more
doaj   +1 more source