Abstract
In this paper the classical convergence theorems by Śleszyński-Pringsheim, Worpitzky and Van Vleck for ordinary continued fractions will be generalized to continued fractions generalizations (along the lines of the Jacobi–Perron algorithm) with four-term recurrence relations.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License ( https://creativecommons.org/licenses/by-nc/2.0 ), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Bruin, M.G.d. ‘Classical’ convergence theorems for generalized continued fractions. Numer Algor 44, 367–380 (2007). https://doi.org/10.1007/s11075-007-9115-1
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DOI: https://doi.org/10.1007/s11075-007-9115-1
Keywords
- Generalized continued fractions
- Jacobi–Perron algorithm
- Recurrence relations
- Linear fractional transformations
- Convergence