Acta mathematica scientia,Series A ›› 2012, Vol. 32 ›› Issue (4): 698-708.

• Articles • Previous Articles     Next Articles

Gautschi-type Inequalities and Their Applications

 CHU Yu-Ming1, ZHANG Xiao-Ming2, SHI Huan-Nan3   

  1. 1.Department of Mathematics and Computing Science, Hunan City University, Hunan Yiyang 413000|2.Haining Radio and TV University, Zhejiang Haining 314400|3.Department of Electronic Information, Bejing Union University, Bejing 100011
  • Received:2010-09-11 Revised:2011-11-15 Online:2012-08-25 Published:2012-08-25
  • Supported by:

    国家自然科学基金(11071069, 11171307)和湖南省自然科学基金(09JJ6003)资助

Abstract:

We established two new Gautschi-type inequalities for the gamma function. As applications, we present the upper and lower bounds for Γ(x+1)/Γ(x+1/2) (x>0) and (2n-1)!!/(2n)!! .

Key words: Gamma function, Gautschi-type inequality, Monotonicity, Convexity

CLC Number: 

  • 33B15
Trendmd