On generalized gamma functions related to the Laurent coefficients of the Riemann zeta function
type: Item
instance of: scholarly article
title: On generalized gamma functions related to the Laurent coefficients of the Riemann zeta function
zbMATH Open document ID: 0811.33001
DOI: 10.1007/BF01837979
author: Karl Dilcher
published in: Aequationes Mathematicae
publication date: 1995-05-04T00:00:00Z
full work available at URL: https://eudml.org/doc/137592
review text: The paper discusses a class of generalized gamma functions \(\Gamma_ k (z)\), defined as a generalization of Euler's limit for the gamma function. The paper concentrates on the numbers \(\gamma_ k\) which, on the one hand, appear as coefficients in the Laurent expansion of the Riemann zeta function at the point 1, and on the other hand as the coefficient of the linear term in the Maclaurin expansion in \(\ln \Gamma_ k(z)\) at \(z=0\). A new series expansion for \(\gamma_ k\) is derived and these and related constants are numerically computed for \(1\leq k\leq 15\).
Mathematics Subject Classification ID: 33B15
Mathematics Subject Classification ID: 11Y60
Mathematics Subject Classification ID: 11M06
zbMATH DE Number: 636043
zbMATH Keywords: generalized gamma functions
zbMATH Keywords: Riemann zeta function
reviewed by: Nico M. Temme
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 636043