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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… Click to show full 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.
Journal Title: Advances in Difference Equations
Year Published: 2019
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