Results 71 to 80 of about 611,264 (163)

ON FUNCTIONAL INEQUALITIES FOR THE PSI FUNCTION

Проблемы анализа
Motivated by the works of Bougotta and Mercer, the authors in this paper study the monotonicity of the function x↦ψ(1+bx)^a/ψ(1+ax)^b, and establish several inequalities involving the psi function.
Barkat A. Bhayo, Liyao Xie, Sebnem Yildiz Yar   +2 more
doaj   +1 more source

Justification of architecture for intelligent agnostic multimodal transportation

Transport Technologies
Urban population growth is estimated to exceed 50% by 2050 in today's urban spaces. Therefore, the mobility patterns of people and objects become a fundamental element for planning, control, and decision-making in multimodal transportation. The use of an
Klaus Serny
doaj   +1 more source

An Elementary Approach to Euler’s Reflection Formula and Its Role in the Infinite Product of the Sine Function and the Basel Problem

Foundations
We present a proof, using elementary methods, of the Euler reflection formula for the Gamma function, based on an integral computed by Laplace and on the Euler–Gauss infinite product representation of Gamma.
Antonio E. Bargellini, Daniele Ritelli
doaj   +1 more source

On the Definition of Higher Gamma Functions

Constructive Approximation
We generalize our previous new definition of Euler Gamma function to higher Gamma functions. With this unified approach, we characterize Barnes higher Gamma functions, Mellin Gamma functions, Barnes multiple Gamma functions, Jackson $q$-Gamma function, and Nishizawa higher $q$-Gamma functions. This approach extends to more general functional equations.
openaire   +4 more sources

REMARKS ON COMPLETE MONOTONICITY OF A FUNCTION INVOLVING THE GAMMA FUNCTION

Проблемы анализа, 2015
In the note, the authors give several remarks on the paper in "Chen and Haigang Zhou On completely monotone of an arbitrary real parameter function involving the gamma function. Applied Mathematics and Compulation, 2014, vol. 242, pp.
F. Qi, B. N. Guo
doaj  

Sharp Smith's bounds for the gamma function. [PDF]

J Inequal Appl, 2018
Li XQ, Liu ZM, Yang ZH, Zheng SZ.
europepmc   +1 more source

Windschitl type approximation formulas for the gamma function. [PDF]

J Inequal Appl, 2018
Yang ZH, Tian JF.
europepmc   +1 more source

An accurate approximation formula for gamma function. [PDF]

J Inequal Appl, 2018
Yang ZH, Tian JF.
europepmc   +1 more source

On rational bounds for the gamma function. [PDF]

J Inequal Appl, 2017
Yang ZH, Qian WM, Chu YM, Zhang W.
europepmc   +1 more source

On Hardy-type integral inequalities with the gamma function. [PDF]

J Inequal Appl, 2017
Liao J, Yang B.
europepmc   +1 more source