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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A monotoneity property of the gamma function


Authors: G. D. Anderson and S.-L. Qiu
Journal: Proc. Amer. Math. Soc. 125 (1997), 3355-3362
MSC (1991): Primary 33B15; Secondary 26A48, 26D07
MathSciNet review: 1425110
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Abstract: In this paper we obtain a monotoneity property for the gamma function that yields sharp asymptotic estimates for $\Gamma (x)$ as $x$ tends to $\infty $, thus proving a conjecture about $\Gamma (x)$.


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Additional Information

G. D. Anderson
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824
Email: anderson@math.msu.edu

S.-L. Qiu
Affiliation: School of Science and Arts, Hangzhou Institute of Electronics Engineering (HIEE), Hangzhou 310037, People’s Republic of China

DOI: http://dx.doi.org/10.1090/S0002-9939-97-04152-X
PII: S 0002-9939(97)04152-X
Keywords: Gamma function, psi function, monotoneity, inequalities
Received by editor(s): June 20, 1996
Communicated by: Hal L. Smith
Article copyright: © Copyright 1997 American Mathematical Society