Displaying similar documents to “A Wirsing-type approach to some continued fraction expansion.”

Continued fractions on the Heisenberg group

Anton Lukyanenko, Joseph Vandehey (2015)

Acta Arithmetica

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We provide a generalization of continued fractions to the Heisenberg group. We prove an explicit estimate on the rate of convergence of the infinite continued fraction and several surprising analogs of classical formulas about continued fractions.

'The mother of all continued fractions'

Karma Dajani, Cor Kraaikamp (2000)

Colloquium Mathematicae

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We give the relationship between regular continued fractions and Lehner fractions, using a procedure known as insertion}. Starting from the regular continued fraction expansion of any real irrational x, when the maximal number of insertions is applied one obtains the Lehner fraction of x. Insertions (and singularizations) show how these (and other) continued fraction expansions are related. We also investigate the relation between Lehner fractions and the Farey expansion (also known...

Continued fraction expansions for complex numbers-a general approach

S. G. Dani (2015)

Acta Arithmetica

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We introduce a general framework for studying continued fraction expansions for complex numbers, and establish some results on the convergence of the corresponding sequence of convergents. For continued fraction expansions with partial quotients in a discrete subring of ℂ an analogue of the classical Lagrange theorem, characterising quadratic surds as numbers with eventually periodic continued fraction expansions, is proved. Monotonicity and exponential growth are established for the...

Simple Continued Fractions and Their Convergents

Bo Li, Yan Zhang, Artur Korniłowicz (2006)

Formalized Mathematics

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The article introduces simple continued fractions. They are defined as an infinite sequence of integers. The characterization of rational numbers in terms of simple continued fractions is shown. We also give definitions of convergents of continued fractions, and several important properties of simple continued fractions and their convergents.