Two families of approximations for the gamma function

In this paper, we establish two families of approximations for the gamma function: where the constants and can be determined by recurrences, and , , are parameters. Numerical comparison shows that our results are more accurate than Stieltjes, Luschny and Nemes’ formulae, which, to our knowledge, are...

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Bibliographic Details
Published inNumerical algorithms Vol. 64; no. 3; pp. 403 - 416
Main Authors Feng, Lei, Wang, Weiping
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.11.2013
Springer Nature B.V
Subjects
Algebra
Algorithms
Approximation
Computer Science
Constants
Gamma function
Mathematical models
Numeric Computing
Numerical Analysis
Original Paper
Theory of Computation
33B15
Stirling’s formula
41A60
Gamma function
Approximations
Online AccessGet full text
ISSN1017-1398
1572-9265
DOI10.1007/s11075-012-9671-x

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Summary:In this paper, we establish two families of approximations for the gamma function: where the constants and can be determined by recurrences, and , , are parameters. Numerical comparison shows that our results are more accurate than Stieltjes, Luschny and Nemes’ formulae, which, to our knowledge, are better than other approximations in the literature.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-012-9671-x