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

 

Remarks on a paper by Chao-Ping Chen and Feng Qi


Author: Stamatis Koumandos
Journal: Proc. Amer. Math. Soc. 134 (2006), 1365-1367
MSC (2000): Primary 33B15; Secondary 26D20
Published electronically: October 6, 2005
MathSciNet review: 2199181
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Abstract: In a recent paper, Chao-Ping Chen and Feng Qi (2005) established sharp upper and lower bounds for the sequence $ P_{n}:=\frac{1.3\ldots (2n-1)}{2.4\ldots 2n}$. We show that their result follows easily from a theorem of G. N Watson published in 1959. We also show that the main result of Chen and Qi's paper is a special case of a more general inequality which admits a very short proof.


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Additional Information

Stamatis Koumandos
Affiliation: Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus
Email: skoumand@ucy.ac.cy

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08104-9
PII: S 0002-9939(05)08104-9
Keywords: Wallis' inequality, Gamma function, monotonicity, best bounds
Received by editor(s): September 15, 2004
Received by editor(s) in revised form: November 30, 2004
Published electronically: October 6, 2005
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2005 American Mathematical Society