Results 51 to 60 of about 681 (108)

Refinements of Some Recent Inequalities for Certain Special Functions

Annales Mathematicae Silesianae, 2019
The aim of this paper is to give some refinements to several inequalities, recently etablished, by P.K. Bhandari and S.K. Bissu in [Inequalities via Hölder’s inequality, Scholars Journal of Research in Mathematics and Computer Science, 2 (2018), no.
Akkouchi Mohamed, Ighachane Mohamed Amine   +1 more
doaj   +1 more source

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
doaj   +1 more source

An alternative proof of Elezovi\'c-Giordano-Pe\v{c}ari\'c's theorem

, 2009
In the present note, an alternative proof is supplied for Theorem~1 in [N. Elezovi\'c, C. Giordano and J. Pe\v{c}ari\'c, \textit{The best bounds in Gautschi's inequality}, Math. Inequal. Appl.
Guo, Bai-Ni, Qi, Feng
core   +1 more source

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

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

Averages of Ramanujan sums: Note on two papers by E. Alkan

, 2014
We give a simple proof and a multivariable generalization of an identity due to E. Alkan concerning a weighted average of the Ramanujan sums. We deduce identities for other weighted averages of the Ramanujan sums with weights concerning logarithms ...
Tóth, László
core   +1 more source

Two monotonic functions involving gamma function and volume of unit ball

, 2010
In present paper, we prove the monotonicity of two functions involving the gamma function $\Gamma(x)$ and relating to the $n$-dimensional volume of the unit ball $\mathbb{B}^n$ in $\mathbb{R}^n$.Comment: 7 ...
Anderson G. D., Bai-Ni Guo, Feng Qi, Guo B.-N., Huo Z.-H., Niu D.-W., Qi F., Qi F., Qi F., Qi F., Qi F., Qi F., Qi F.   +12 more
core   +1 more source

On the harmonic number expansion by Ramanujan

, 2013
Let γ=0.577215664… denote the Euler-Mascheroni constant, and let the sequences The main aim of this paper is to find the values r, s, t, a, b, c and d which provide the fastest sequences (un)n≥1 and (vn)n≥1 approximating the Euler-Mascheroni constant.
C. Mortici, Chao-Ping Chen
semanticscholar   +1 more source

Integral representation of some functions related to the Gamma function

, 2004
We prove that the functions Phi(x)=[Gamma(x+1)]^{1/x}(1+1/x)^x/x and log Phi(x) are Stieltjes ...
Berg, Christian
core   +1 more source

A complete monotonicity property of the multiple gamma function

, 2020
We consider the following functions fn (x) = 1− ln x + lnGn (x +1) x and gn (x) = x Gn (x +1) x , x ∈ (0,∞), n ∈N, where Gn (z) = (Γn (z))(−1) and Γn is the multiple gamma function of order n. In this work, our aim is to establish that f (2n) 2n (x) and (
Sourav Das
semanticscholar   +1 more source