New refinements of some classical inequalities
نویسندگان
چکیده
منابع مشابه
Refinements of Some Partition Inequalities
In the present paper we initiate the study of a certain kind of partition inequality, by showing, for example, that if M 5 is an integer and the integers a and b are relatively prime to M and satisfy 1 a < b < M/2, and the c(m,n) are defined by 1 (sqa, sqM a; qM )1 1 (sqb, sqM b; qM )1 := X
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In the article, some Huygens inequalities involving trigonometric and hyperbolic functions are refined and sharpened. Mathematics subject classification (2010): Primary 26D05; Secondary 33B10.
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Zhengjie Sun and Ling Zhu Department of Mathematics, Zhejiang Gongshang University, Zhejiang, Hangzhou 310018, China Correspondence should be addressed to Ling Zhu, [email protected] Received 22 August 2011; Accepted 4 October 2011 Academic Editor: Morteza Rafei Copyright q 2011 Z. Sun and L. Zhu. This is an open access article distributed under the Creative Commons Attribution License, which...
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15 صفحه اولStirling’s Formula Revisited via Some Classical and New Inequalities
The Hermite-Hadamard inequality is used to develop an approximation to the logarithm of the gamma function which is more accurate than the Stirling approximation and easier to derive. Then the concavity of the logarithm of gamma of logarithm is proved and applied to the Jensen inequality. Finally, the Wallis ratio is used to obtain the additional term in Stirling’s approximation formula. Mathem...
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2009
ISSN: 1331-4343
DOI: 10.7153/mia-12-39