A new asymptotic series for the Gamma function

The famous Stirling's formula says that Γ ( s + 1 ) = 2 π s ( s / e ) s e γ ( s ) = 2 π ( s / e ) s e θ ( s ) / 12 s . In this paper, we obtain a novel convergent asymptotic series of γ ( s ) and proved that θ ( s ) is increasing for s > 0 .

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Bibliographic Details
Published inJournal of computational and applied mathematics Vol. 195; no. 1; pp. 134 - 154
Main Authors Shi, Xiquan, Liu, Fengshan, Hu, Minghan
Format Journal Article Conference Proceeding
LanguageEnglish
Published Amsterdam Elsevier B.V 15.10.2006
Elsevier
Subjects
Asymptotic series
Classical combinatorial problems
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Gamma function
Mathematical analysis
Mathematics
Sciences and techniques of general use
Special functions
Stirling formula
33B15
Asymptotic series
Stirling formula
05A16
Gamma function
33B15;05A16
Applied mathematics
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Summary:The famous Stirling's formula says that Γ ( s + 1 ) = 2 π s ( s / e ) s e γ ( s ) = 2 π ( s / e ) s e θ ( s ) / 12 s . In this paper, we obtain a novel convergent asymptotic series of γ ( s ) and proved that θ ( s ) is increasing for s > 0 .
Bibliography:SourceType-Scholarly Journals-2
ObjectType-Feature-2
ObjectType-Conference Paper-1
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SourceType-Conference Papers & Proceedings-1
ObjectType-Article-3
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2005.03.081