Canonical products of small order and related Pick functions
type: Item
instance of: scholarly article
title: Canonical products of small order and related Pick functions
zbMATH Open document ID: 1067.30076
author: Henrik L. Pedersen
published in: Journal of Computational and Applied Mathematics
publication date: 2005-02-23T00:00:00Z
review text: The authors consider canonical products \[ P_\rho (z)=\prod_{n=1}^\infty(1+z/n^\rho),\quad\rho>1 \] and \[ Q(z)=\prod_{n=0}^\infty(1+zq^n),\quad q\in(0,1). \] It is shown that \((\log P_\rho(z))/z^{1/\rho}\) and \((\log Q(z)-\log Q(-q))/{\text{ Log}}\,((1+z)/(1-z))\) are Pick functions. Applications are found.
reviewed by: Vladimir V. Peller
Mathematics Subject Classification ID: 30E20
Mathematics Subject Classification ID: 33D05
zbMATH DE Number: 2137452
zbMATH Keywords: canonical product
zbMATH Keywords: Pick function
zbMATH Keywords: completely monotone function
zbMATH Keywords: \(q\)-gamma function
MaRDI profile type: Publication
full work available at URL: j.cam.2004.05.011
OpenAlex ID: W2039640475
cites work: Sharp bounds for the ratio of \(q\)-gamma functions
cites work: A monotoneity property of the gamma function
cites work: Seminaire de théorie du potentiel, Paris, No.5. Directeurs: M. Brelot, G. Choquet et J. Deny. Redacteurs: F. Hirsch et G. Mokobodzki
cites work: Pick functions related to the gamma function.
cites work: Q5833361
cites work: Q4405419
cites work: Q4527133
cites work: Q3994552
cites work: Q4896037
cites work: The double gamma function and related Pick functions.
cites work: Pick functions related to entire functions having negative zeros
cites work: Q5846853
DOI: 10.1016/J.CAM.2004.05.011
description: scientific article; zbMATH DE number 2137452