Order and type of entire functions arising from separately convergent continued fractions
type: Item
instance of: scholarly article
title: Order and type of entire functions arising from separately convergent continued fractions
zbMATH Open document ID: 0715.30005
DOI: 10.1016/0377-0427(90)90437-5
author: W. J. Thron
published in: Journal of Computational and Applied Mathematics
publication date: 1990-01-01T00:00:00Z
review text: 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).
Mathematics Subject Classification ID: 30B70
Mathematics Subject Classification ID: 30D20
zbMATH DE Number: 4177459
zbMATH Keywords: separate convergence
zbMATH Keywords: order
zbMATH Keywords: type
MaRDI profile type: Publication
full work available at URL: 0377-0427(90)90437-5
OpenAlex ID: W2069148843
cites work: Q4732836
cites work: Q3496443
description: scientific article; zbMATH DE number 4177459