Title
The Riemann <tex>$\zeta$</tex> function and asymptotics for Stieltjes fractions The Riemann <tex>$\zeta$</tex> function and asymptotics for Stieltjes fractions
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Subject
Mathematics
Source (journal)
Ramanujan journal
Volume/pages
21(2010) :1 , p. 1-16
ISSN
1382-4090
ISI
000274043700001
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
We study the asymptotic behaviour of the coefficients in the continued fractions corresponding to Stieltjes transforms of weight functions on a finite interval. It is shown that, in general, the coefficients with odd and even index converge to a different limit. For a specific class of weights a detailed asymptotic expansion of the coefficients is obtained. Some examples serve as illustration and an application to continued fraction expansions for the Riemann zeta function is given.
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