On the relationship between generalised continued fractions and G-continued fractions

摘要

In this paper the connection between generalised continued fractions (de Bruin 1974)) and G-continued fractions (Levrie (1988)) is studied. This connection is used to prove a convergence theorem for generalised continued fractions and to accelerate the convergence of generalised continued fractions associated with a class of linear recurrence relations of Poincaré-type.