The Experts below are selected from a list of 18066 Experts worldwide ranked by ideXlab platform
Xiaoguang Wang - One of the best experts on this subject based on the ideXlab platform.
-
a new asymptotic expansion and some inequalities for the gamma Function
Journal of Number Theory, 2014Co-Authors: Xiaoguang WangAbstract:Abstract In this paper, based on the Burnside formula, an asymptotic expansion of the Factorial Function and some inequalities for the gamma Function are established. Finally, for demonstrating the superiority of our new series over the Burnside formula, the classical Stirling series and the Mortici sequences, some numerical computations are given.
Radić Grgur - One of the best experts on this subject based on the ideXlab platform.
-
Application Program for Analysis of Asymptotic Expansions for Factorial Function
University of Zagreb. Faculty of Electrical Engineering and Computing., 2019Co-Authors: Radić GrgurAbstract:Glavna tema rada je prikaz i analiza poznatih asimptotskih razvoja gama funkcije. Uz primjenu nove metode Burić-Elezović omogućeno je povezivanje i poopćavanje te poboljšanje mnogih poznatih aproksimacijskih formula Stirlingovog tipa čime su dobivene nove veoma točne aproksimacije za faktorijelnu funkciju. Prvo poglavlje je posvećeno gama funkciji te njena veza s faktorijelnom funkcijom. Također, analiziraju se Bernoullijevi polinomi. U drugom poglavlju definirani su asimptotski redovi te proučeni poznati razvoji gama funkcije Stirlingovog tipa te poopćenje i poboljšanje istih. Prezentirani su razni numerički rezultati navedenih formula. U posljednjem, trećem poglavlju, opisivat će se programska aplikacija koja je pridružena radu.The main topic of the paper is the presentation and analysis of known asymptotic expansions of gamma Function. With the application of the new Burić-Elezović method it is possible to connect, amplify and improve many known Stirling's type approximation formulas, resulting in new very accurate approximations for Factorial Function. The first chapter is devoted to the gamma Function and its relationship to the Factorial Function. There are also analyzed Bernoulli's polynomials. In the second chapter, asymptotic rows were defined and studied well-known Stirling's type asymptotic expansions of the gamma Function and its generalization with enhancements. Numerical results of the above formulas have been presented. In the last, third chapter, a application program that is associated with the thesis will be described
Cristinel Mortici - One of the best experts on this subject based on the ideXlab platform.
-
NEW SHARP INEQUALITIES FOR APPROXIMATING THE Factorial Function AND THE DIGAMMA Function
Miskolc Mathematical Notes, 2010Co-Authors: Cristinel MorticiAbstract:The aim of this paper is to establish new sharp upper and lower bounds for the gamma and digamma Functions, starting from the Stirling's formula. 2000 Mathematics Subject Classification: 30E15, 26D07, 41A60
-
an ultimate extremely accurate formula for approximation of the Factorial Function
Archiv der Mathematik, 2009Co-Authors: Cristinel MorticiAbstract:We prove in this paper that for every x ≥ 0, $$\sqrt{2\pi e}\cdot e^{-\omega}\left( \frac{x+\omega}{e}\right) ^{x+\frac {1}{2}} < \Gamma(x+1)\leq\alpha\cdot\sqrt{2\pi e}\cdot e^{-\omega}\left( \frac{x+\omega}{e}\right)^{x+\frac{1}{2}}$$ where \({\omega=(3-\sqrt{3})/6}\) and α = 1.072042464..., then $$\beta\cdot\sqrt{2\pi e}\cdot e^{-\zeta}\left(\frac{x+\zeta}{e}\right)^{x+\frac{1}{2}}\leq\Gamma(x+1) < \sqrt{2\pi e}\cdot e^{-\zeta}\left( \frac{x+\zeta}{e}\right)^{x+\frac{1}{2}},$$ where \({\zeta=(3+\sqrt{3})/6}\) and β = 0.988503589... Besides the simplicity, our new formulas are very accurate, if we take into account that they are much stronger than Burnside’s formula, which is considered one of the best approximation formulas ever known having a simple form.
Klimek, Matthew D. - One of the best experts on this subject based on the ideXlab platform.
-
A new entire Factorial Function
2021Co-Authors: Klimek, Matthew D.Abstract:We introduce a new Factorial Function which agrees with the usual Euler gamma Function at both the positive integers and at all half-integers, but which is also entire. We describe the basic features of this Function.Comment: 3 pages, 2 figure
D H Fowler - One of the best experts on this subject based on the ideXlab platform.
-
the Factorial Function stirling s formula
The Mathematical Gazette, 2000Co-Authors: D H FowlerAbstract:How big is n!? For example, to pluck a number out of thin air, what is the order of magnitude of 272! ? This is the third note of a series on the Factorial. The two previous notes [1] and [2] dealt with the Factorial Function x! while here we only consider n! when n is an integer, but its main results also apply to non-integer arguments. This note is longer and more elaborate than the previous ones, but the principal result is in the opening section. Only aficionados need go any further.
