Order and type of entire functions arising from separately convergent continued fractions
In a paper from 1888, J. Śleszyński investigated continued fractions \[ K\frac{a_ nz}{1}\text{ where } \sum^{\infty}_{n=1}| a_ n| <\infty \] with approximants \(f_ n(z)=A_ n(z)/B_ n(z)\). He proved that not only do \(\{f_ n(z)\}\) converge, but \(\{A_ n(z)\}\) and \(\{B_ n(z)\}\) both converge locally uniformly in \({\mathbb{C}}\) to entire functions A(z) and B(z). Inspired by two inequalities in Śleszyński's paper, the author derives information about the order and type of the limit functions A(z) and B(z).
scientific article; zbMATH DE number 4177459