Canonical products of small order and related Pick functions
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摘要
We show that various functions related to the logarithms of the canonical products Pρ(z)=∏n=1∞(1+z/nρ), ρ>1 and Q(z)=∏n=0∞(1+zqn), q∈(0,1) are Pick functions. As a consequence we find an integral expansion of a function involving the logarithm of Jacksons q-gamma function.
论文关键词：Primary 30E20,Secondary 33D05,Pick function,Completely monotone function,q-gamma function
论文评审过程：Received 23 October 2003, Revised 1 April 2004, Available online 14 July 2004.
论文官网地址：https://doi.org/10.1016/j.cam.2004.05.011
