Order and type of entire functions arising from separately convergent continued fractions

摘要

In 1888 Śleszyński proved that if Σ⨍an⨍ <∞, then the numerators An(z) and denominators Bn(z) of the approximants of the regular C-fraction K(anz/1) converge separately to entire functions. Here we present results about the order and type of these functions.