Repeated modifications of limit k-periodic continued fractions (Q1058256)

The convergence of limit k-periodic continued fractions \(K(a_ n/b_ n)\) can be accelerated by modifying the approximants by means of the tails of an auxiliary periodic continued fraction. Such a modification can also be used to continue a function \(K(a_ n(z)/b_ n(z))\) meromorphically. In this article is described a method for repeating this process and thereby obtain stronger results. It generalizes the method introduced by \textit{W. J. Thron} and \textit{H. Waadeland} [Analytic theory of continued fractions, Proc. Semin.-Workshop, Loen/Norw. 1981, Lect. Notes Math. 932, 225-240 (1982; Zbl 0497.30011)].