Generalized continued fractions: a unified definition and a Pringsheim-type convergence criterion. (English) Zbl 1485.40003
Summary: 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.
MSC:
| 40A15 | Convergence and divergence of continued fractions |
| 11A55 | Continued fractions |
| 11J70 | Continued fractions and generalizations |
Keywords:
generalized continued fractions; continued fractions in Banach algebras; matrix continued fractions; convergence criteria; Pringsheim-type convergence criterionReferences:
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