A Two-Sided Inequality of Gamma Function
Received:March 28, 2005  Revised:June 09, 2005
Key Words: two-sided inequality   Gamma function   Stirling formula.  
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Author NameAffiliation
WANG Fan Special Class for the Gifted Young, University of Science and Technology of China, Anhui 230026, China 
ZHAO Yun-peng Special Class for the Gifted Young, University of Science and Technology of China, Anhui 230026, China 
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Abstract:
      This note shows that the inequality \[ (\frac{x}{e})^x\sqrt {2\pi x} (1+\frac{1}{12x})<\Gamma (x+1)<(\frac{x}{e})^x\sqrt {2\pi x} (1+\frac{1}{12x-0.5})\] holds for all $x\ge 1$.
Citation:
DOI:10.3770/j.issn:1000-341X.2007.04.001
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