Results 61 to 70 of about 681 (108)

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 exact constants for the approximation of the quantity in the Wallis’ formula

, 2013
In this article, a sharp two-sided bounding inequality and some best constants for the approximation of the quantity associated with the Wallis’ formula are presented.MSC:41A44, 26D20, 33B15.
Senlin Guo, Jian-guo Xu, Feng Qi (祁锋)   +2 more
semanticscholar   +1 more source

Inequalities Involving $q$-Analogue of Multiple Psi Functions

, 2020
Logarithmic derivative of the multiple gamma function is known as the multiple psi function. In this work q-analogue of multiple psi functions of order n have been considered.
Sourav Das
semanticscholar   +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  

New inequalities for the volume of the unit ball in ℝ^n

, 2017
Many interesting monotonicity properties and inequalities for the volume of the unit ball in Rn have been established. The main object of this paper is to establish new inequalities for the volume of the unit ball in Rn .
Tao Ban, Chao Chen
semanticscholar   +1 more source

Sharp estimates regarding the remainder of the alternating harmonic series

, 2015
In the present paper we obtain enhanced estimates regarding the remainder of the alternating harmonic series. More precisely, we show that 1 4n2 +a < ∣ ∣∣ ∣ ∣ n ∑ k=1 (−1)k−1 1 k − (−1)n−1 1 2n − ln2 ∣ ∣∣ ∣ ∣ 1 4n2 +b , for all n ∈N , with a = 2 and b ...
A. Sîntămărian
semanticscholar   +1 more source

Asymptotic formulas for the gamma function by Gosper

, 2015
The main aim of this paper is to give two general asymptotic expansions for the gamma function, which include the Gosper formula as their special cases. Furthermore, we present an inequality for the gamma function.
Long Lin, Chao Chen
semanticscholar   +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

Asymptotic expansions of the multiple quotients of gamma functions with applications

, 2013
Asymptotic expansions of the multiple quotients of two gamma functions are obtained and analyzed. We apply these results to the hypergeometric function and central multinomial coefficient which leads to the new approximation formulas. Mathematics subject
Tomislav Buric, N. Elezovic, Ratko Šimić   +2 more
semanticscholar   +1 more source

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