Generalized continued fractions: a unified definition and a Pringsheim-type convergence criterion

Autor:	Hendrik Baumann
Jazyk:	angličtina
Rok vydání:	2019
Předmět:	Generalized continued fractions Continued fractions in Banach algebras Matrix continued fractions Convergence criteria Pringsheim-type convergence criterion Mathematics QA1-939
Zdroj:	Advances in Difference Equations, Vol 2019, Iss 1, Pp 1-30 (2019)
Druh dokumentu:	article
ISSN:	1687-1847
DOI:	10.1186/s13662-019-2340-9
Popis:	Abstract In the literature, many generalizations of continued fractions have been introduced, and for each of them, convergence results have been proved. In this paper, we suggest a definition of generalized continued fractions which covers a great variety of former generalizations as special cases. As a starting point for a convergence theory, we prove a Pringsheim-type convergence criterion which includes criteria for the aforementioned special cases. Furthermore, we address several fields in which our definition may be applied.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/659e30227a4a4d8a8b98976c4d4d1b5a Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
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