The double gamma function and related Pick functions

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摘要

Denoting by G the Barnes double gamma function we find the Stieltjes representation of the related Pick functionz↦logG(z+1)z2Logz.As a corollary we obtain that this function has a completely monotone derivative on the positive half line.

论文关键词：primary 30E20,secondary 30D15,30E15,33B15,Double gamma function,Pick function,Integral representation

论文评审过程：Received 5 November 2001, Revised 10 May 2002, Available online 11 December 2002.

论文官网地址：https://doi.org/10.1016/S0377-0427(02)00604-0