The Riemann <tex>$\zeta$</tex> function and asymptotics for Stieltjes fractions
Faculty of Sciences. Mathematics and Computer Science
, p. 1-16
University of Antwerp
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.