Title The Riemann $\zeta$ function and asymptotics for Stieltjes fractions Author Van Deun, Joris Faculty/Department Faculty of Sciences. Mathematics and Computer Science Publication type article Publication 2010 2010 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. E-info http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000274043700001&DestLinkType=RelatedRecords&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000274043700001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=ef845e08c439e550330acc77c7d2d848 Handle