Functional equations for the Stieltjes constants View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2016-04

AUTHORS

Mark W. Coffey

ABSTRACT

The Stieltjes constants γk(a) appear as the coefficients in the regular part of the Laurent expansion of the Hurwitz zeta function ζ(s,a) about s=1. We present the evaluation of γ1(a) and γ2(a) at rational arguments, this being of interest to theoretical and computational analytic number theory and elsewhere. We give multiplication formulas for γ0(a), γ1(a), and γ2(a), and point out that these formulas are cases of an addition formula previously presented. We present certain integral evaluations generalizing Gauss’ formula for the digamma function at rational argument. In addition, we give the asymptotic form of γk(a) as a→0 as well as a novel technique for evaluating integrals with integrands with ln(-lnx) and rational factors. More... »

PAGES

577-601

Journal

TITLE

The Ramanujan Journal

ISSUE

3

VOLUME

39

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11139-015-9691-y

DOI

http://dx.doi.org/10.1007/s11139-015-9691-y

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1029610458


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