## 28 Citations

On the asymptotic expansions of the gamma function related to the Nemes, Gosper and Burnside formulas

- MathematicsAppl. Math. Comput.
- 2016

Inequalities, asymptotic expansions and completely monotonic functions related to the gamma function

- MathematicsAppl. Math. Comput.
- 2015

Inequalities and asymptotic expansions associated with the Ramanujan and Nemes formulas for the gamma function

- MathematicsAppl. Math. Comput.
- 2015

Asymptotic expansions of the gamma function related to Windschitl's formula

- MathematicsAppl. Math. Comput.
- 2014

Asymptotic formulas for the gamma function by Gosper

- Mathematics, Philosophy
- 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…

ASYMPTOTIC EXPANSIONS OF THE GAMMA FUNCTION ASSOCIATED WITH THE WINDSCHITL AND SMITH FORMULAS

- Mathematics
- 2014

In this paper, we develop the Windschitl and Smith formulas for the gamma function to complete asymptotic expansions and provide explicit formulas for determining the coefficients of these asymptotic…

A new fast asymptotic series for the gamma function

- Mathematics
- 2015

It is the scope of this paper to present a new formula for approximating the gamma function. The importance of this new formula consists in the fact that the convergence of the corresponding…

Efficient approximations of the gamma function and further properties

- Mathematics
- 2017

The aim of this paper is to introduce some simple and fast formulas for approximating the gamma function. Some involved functions are completely monotonic. The corresponding asymptotic series are…

A New Asymptotic Series and Estimates Related to Euler Mascheroni Constant

- Mathematics
- 2020

In this article, we give a new asymptotic series and some estimates for a sequence that converges to Euler-Mascheroni's constant.

## References

SHOWING 1-10 OF 14 REFERENCES

On Ramanujan's Double Inequality for the Gamma Function

- Mathematics
- 2003

Ramanujan presented (without proof) the following double inequality for the gamma function: π(xe)x[8x3+4x2+x+1100]1/6

VERY ACCURATE APPROXIMATIONS FOR THE FACTORIAL FUNCTION

- Mathematics
- 2010

We establish the following new Stirling-type approximation formulas for the factorial function n! ≈ √ 2πn n e −n n+ 1 + 1

New asymptotic expansion for the Gamma function

- Mathematics
- 2010

Using a series transformation, the Stirling-De Moivre asymptotic series approximation to the Gamma function is converted into a new one with better convergence properties. The new formula is being…

SHARP INEQUALITIES FOR FACTORIAL n

- Mathematics
- 2008

Let n be a positive integer. We provewith the best possible constantsα = 1 - 2πe-2 = 0.149663... and β = 1/6 = 0.1666666...This refines and extends a result of Sandor and Debnath, who proved that the…

Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables

- Mathematics
- 1964

A handbook of mathematical functions that is designed to provide scientific investigations with a comprehensive and self-contained summary of the mathematical functions that arise in physical and…

Asymptotic Expansions—I

- Mathematics
- 2006

The interest in asymptotic analysis originated from the necessity of searching for approximations to functions close the point(s) of interest. Suppose we have a function f(x) of single real parameter…

Decision procedure for indefinite hypergeometric summation

- Mathematics
- 1978

Abstract
Given a summand an, we seek the “indefinite sum” S(n) determined (within an additive constant) by [Formula: see text] or, equivalently, by [Formula: see text] An algorithm is exhibited…