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Other Generalizations of Continued Fractions

Algorithms and Computation in Mathematics, 2013
In this chapter we present some other generalizations of regular continued fractions to the multidimensional case. The main goal for us here is to give different geometric constructions related to such continued fractions (whenever possible). We say a few words about Minkowski–Voronoi continued fractions, triangle sequences related to Farey addition, O’
Oleg Karpenkov
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On some generalizations of Ramanujan’s continued fraction identities

Proceedings of the Indian Academy of Sciences - Section A, 1987
Many of the continued fraction expansions of Ramanujan can be viewed as special cases of the expansion of the ratio of basic hypergeometric series: \(_ 2\phi_ 1(a,b;c;xq)/_ 2\phi_ 1(a,b;c;x).\) The authors find the related expansions for the ratios in which the numerator has been replaced by one of a number of similar basic hypergeometric series.
Chandrashekar Adiga, D D Somashekara
exaly   +3 more sources

A Worpitzky theorem for vector valued continued fractions [PDF]

Journal of Computational and Applied Mathematics, 2003
Generalizations of Worpitzky's convergence theorem for ordinary continued fractions are proved for vector valued continued fractions defined by the Samelson inverse for vectors.
Zhu, Gongqin, Zhao, Huanxi, Huanxi Zhao, Gongqin Zhu   +3 more
exaly   +2 more sources

Convergence Theorems for Continued Fractions in Banach Spaces [PDF]

Journal of Approximation Theory, 1996
Generalizations of Śleszyński–Pringheim's convergence criteria for ordinary continued fractions are proved for noncommutative continued fractions in Banach spaces.
Schelling, Andreas
exaly   +2 more sources

Generalization of continued fractions. I

Journal of Mathematical Sciences, 2012
We constructed a new algebraic object, namely, recursion fractions of the n th order that are n -dimensional generalizations of continued fractions. For the representation and the study of such fractions, we used paradeterminants and triangular matrices.
D. I. Bodnar, R. A. Zators’kyi
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Generalized continued fractions

Applied Mathematics and Computation, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Khintchine constants for generalized continued fractions

Applied Mathematics and Computation, 2003
The authors study the limiting behaviour of the Khintchine constants for generalized continued fractions by computer simulations.
Geon Ho Choe, Chihurn Kim
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Convergence acceleration for generalized continued fractions

Transactions of the American Mathematical Society, 1988
The main result in this paper is the proof of convergence acceleration for a suitable modification (as defined by de Bruin and Jacobsen) in the case of an n n
Levrie, Paul, Jacobsen, Lisa
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Generalized continued fractions

Discrete Mathematics and Applications, 1998
The author considers a generalized continued fraction whose expression has the form \[ a_0+\frac{(-1)^{u_1}}{a_1+{\displaystyle \frac{(-1)^{u_2}}{a_2+{\displaystyle \frac{(-1)^{u_3}}{a_3+\dots}}}}}, \] where \(a_i\in\mathbb R\) (\(i=0,1,2,\dots\)) and \(u_i\in\{0,1\}\) (\(i=1,2,\dots\)). In this paper the concept how to represent a real number \(\alpha\
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Stable Evaluation of Generalized Continued Fractions

SIAM Journal on Numerical Analysis, 1981
An error analysis is given for the backward recurrence algorithm for generalized continued fractions. Bounds for the accumulated relative rounding error can be obtained by applying an extension of a technique by Jones and Thron [Math. Comp., 28 (1974), pp. 795–810].
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