Sharp bounds for gamma and digamma function arising from Burnside's formula
The main aim of this paper is to improve the Burnside's formula for approximating the factorial function. We prove the complete monotonicity of a function involving the gamma function to establish new lower and upper sharp bounds for the gamma and digamma function.
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Publishing House of the Romanian Academy
2010-02-01
|
| Series: | Journal of Numerical Analysis and Approximation Theory |
| Subjects: | |
| Online Access: | https://ictp.acad.ro/jnaat/journal/article/view/920 |
| _version_ | 1811291492083302400 |
|---|---|
| author | Cristinel Mortici |
| author_facet | Cristinel Mortici |
| author_sort | Cristinel Mortici |
| collection | DOAJ |
| description | The main aim of this paper is to improve the Burnside's formula for approximating the factorial function. We prove the complete monotonicity of a function involving the gamma function to establish new lower and upper sharp bounds for the gamma and digamma function. |
| first_indexed | 2024-04-13T04:30:14Z |
| format | Article |
| id | doaj.art-25d520e0b14743b08f51750e0f1c8051 |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-04-13T04:30:14Z |
| publishDate | 2010-02-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-25d520e0b14743b08f51750e0f1c80512022-12-22T03:02:21ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2010-02-01391Sharp bounds for gamma and digamma function arising from Burnside's formulaCristinel Mortici0Valahia University of TârgovişteThe main aim of this paper is to improve the Burnside's formula for approximating the factorial function. We prove the complete monotonicity of a function involving the gamma function to establish new lower and upper sharp bounds for the gamma and digamma function.https://ictp.acad.ro/jnaat/journal/article/view/920factorial \(n\)Stirling's formulaBurnside's formulacomplete monotonicityEuler-Mascheroni constantsharp inequalities |
| spellingShingle | Cristinel Mortici Sharp bounds for gamma and digamma function arising from Burnside's formula Journal of Numerical Analysis and Approximation Theory factorial \(n\) Stirling's formula Burnside's formula complete monotonicity Euler-Mascheroni constant sharp inequalities |
| title | Sharp bounds for gamma and digamma function arising from Burnside's formula |
| title_full | Sharp bounds for gamma and digamma function arising from Burnside's formula |
| title_fullStr | Sharp bounds for gamma and digamma function arising from Burnside's formula |
| title_full_unstemmed | Sharp bounds for gamma and digamma function arising from Burnside's formula |
| title_short | Sharp bounds for gamma and digamma function arising from Burnside's formula |
| title_sort | sharp bounds for gamma and digamma function arising from burnside s formula |
| topic | factorial \(n\) Stirling's formula Burnside's formula complete monotonicity Euler-Mascheroni constant sharp inequalities |
| url | https://ictp.acad.ro/jnaat/journal/article/view/920 |
| work_keys_str_mv | AT cristinelmortici sharpboundsforgammaanddigammafunctionarisingfromburnsidesformula |