Results 21 to 30 of about 5,022,265 (207)
Lattice Paths and Branched Continued Fractions: An Infinite Sequence of Generalizations of the Stieltjes–Rogers and Thron–Rogers Polynomials, with Coefficientwise Hankel-Total Positivity [PDF]
Memoirs of the American Mathematical Society, 2018 We define an infinite sequence of generalizations, parametrized by an integer m ≥ 1 m \ge 1 , of the Stieltjes–Rogers and Thron–Rogers polynomials; they arise as the power-series expansions of some branched continued fractions, and as the ...
Mathias Pétréolle +2 more
semanticscholar +1 more source
Generalized continued fractions: a unified definition and a Pringsheim-type convergence criterion
Advances in Difference Equations, 2019 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 ...
Hendrik Baumann
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Continued $\mathbf{A_2}$-fractions and singular functions
Математичні Студії, 2022 In the article we deepen the metric component of theory of infinite $A_2$-continued fractions $[0;a_1,a_2,...,a_n,...]$ with a two-element alphabet $A_2=\{\frac12,1\}$, $a_n\in A_2$ and establish the normal property of numbers of the segment $I=[\frac12 ...
M.V. Pratsiovytyi +3 more
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Commensurable continued fractions [PDF]
, 2013 We compare two families of continued fractions algorithms, the symmetrized Rosen algorithm and the Veech algorithm. Each of these algorithms expands real numbers in terms of certain algebraic integers.
Arnoux, Pierre, Schmidt, Thomas A.
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Geodesic continued fractions and LLL [PDF]
, 2013 We discuss a proposal for a continued fraction-like algorithm to determine simultaneous rational approximations to $d$ real numbers $\alpha_1,\ldots,\alpha_d$. It combines an algorithm of Hermite and Lagarias with ideas from LLL-reduction. We dynamically
Beukers, Frits
core +1 more source
Journal of Approximation Theory, 1999 The matrix continued fraction of a function defined by its power series in \({1\over z}\) with matrix coefficients of dimension \(p\times q\) is presented as a generalisation of \(P\)-fraction. The authors give an algorithm to built the above fraction which corresponds to the extension of the Euler-Jacobi-Perron algorithm.
Sorokin, Vladimir N. +1 more
openaire +2 more sources
An effective criterion for periodicity of ℓ-adic continued fractions [PDF]
Mathematics of Computation, 2018 The theory of continued fractions has been generalized to l-adic numbers by several authors and presents many differences with respect to the real case.
L. Capuano, F. Veneziano, U. Zannier
semanticscholar +1 more source
Continued fractions and transcendental numbers [PDF]
, 2005 It is widely believed that the continued fraction expansion of every irrational algebraic number $\alpha$ either is eventually periodic (and we know that this is the case if and only if $\alpha$ is a quadratic irrational), or it contains arbitrarily ...
Adamczewski, Boris +2 more
core +3 more sources
Location of approximations of a Markoff theorem
International Journal of Mathematics and Mathematical Sciences, 1990 Relative to the first two theorems of the well known Markoff Chain (J.W.S. Cassels, An introduction to diophantine approximation approximations are well located.
K. C. Prasad, M. Lari, P. Singh
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Geodesic Rosen Continued Fractions [PDF]
, 2015 We describe how to represent Rosen continued fractions by paths in a class of graphs that arise naturally in hyperbolic geometry. This representation gives insight into Rosen's original work about words in Hecke groups, and it also helps us to identify ...
Short, Ian, Walker, Mairi
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