The reciprocal of the geometric mean of many positive numbers is a Stieltjes transform

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• 作者：Feng Qi^a ; ^b ; ^c ; ^{qifeng618@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; ^{qifeng618@hotmail.com" class="auth_mail" title="E-mail the corresponding author} ; ^{qifeng618@qq.com" class="auth_mail" title="E-mail the corresponding author} ; ; Bai-Ni Guo^d ; ^{bai.ni.guo@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; ^{bai.ni.guo@hotmail.com" class="auth_mail" title="E-mail the corresponding author} ;
• 关键词：primary ; 30E20 ; secondary ; 26E60 ; 44A15 ; 44A20
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：311
• 期：Complete
• 页码：165-170
• 全文大小：383 K

文摘

In the paper, by the Cauchy integral formula in the theory of complex functions, an integral representation for the reciprocal of the geometric mean of many positive numbers is established. As a result, the reciprocal of the geometric mean of many positive numbers is verified to be a Stieltjes transform and, consequently, a (logarithmically) completely monotonic function.