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Some identities of G-continued fractions and generalized continued fractions [PDF]
Journal of Computational and Applied Mathematics, 1994 Generalized continued fractions and \(G\)-continued fractions are two different types of generalizations of continued fractions, the first one due to M. G. de Bruin, the second one introduced by P. Levrie and R. Piessens. Both types are related to higher order linear recurrence relations (whereas the ordinary ones are related to second order relations).
Paul Levrie
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Generalized Orthogonality and Continued Fractions
Journal of Approximation Theory, 1995 The connection between continued fractions and orthogonality which is familiar for $J$-fractions and $T$-fractions is extended to what we call $R$-fractions of type I and II. These continued fractions are associated with recurrence relations that correspond to multipoint rational interpolants. A Favard type theorem is proved for each type.
Ismail, M.E.H., Masson, D.R.
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Generalized palindromic continued fractions [PDF]
Rocky Mountain Journal of Mathematics, 2018 11 pages, no figures.
David M Freeman
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‘Classical’ convergence theorems for generalized continued fractions [PDF]
Numerical Algorithms, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Marcel G de Bruin
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Tilings, Quasicrystals, Discrete Planes, Generalized Substitutions, and Multidimensional Continued Fractions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 The aim of this paper is to give an overview of recent results about tilings, discrete approximations of lines and planes, and Markov partitions for toral automorphisms.The main tool is a generalization of the notion of substitution.
Pierre Arnoux +3 more
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Computational Triangulation in Mathematics Teacher Education
Computation, 2023 The paper is written to demonstrate the applicability of the notion of triangulation typically used in social sciences research to computationally enhance the mathematics education of future K-12 teachers. The paper starts with the so-called Brain Teaser
Sergei Abramovich
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Mathematics, 2022 The paper promotes the notion of computational experiment supported by a multi-tool digital environment as a means of the development of new mathematical knowledge in the context of education. The main study of the paper deals with the issues of teaching
Sergei Abramovich
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On the Generalized Rogers-Ramanujan Continued Fraction [PDF]
The Ramanujan Journal, 2003 The generalized Rogers-Ramanujan continued fraction is defined for \(| q|< 1\) and any complex \(a\) by \[ R(a,q)= {1\over 1}{\;\atop +} {aq\over 1}{\;\atop +} {aq^2\over 1}{\;\atop +} {aq^3\over 1}{\;\atop +}\cdots. \] The authors prove an asymptotic formula stated by Ramanujan for \(R(a,e^{-x})\) as \(x\to 0+\).
Berndt, Bruce C., Yee, Ae Ja
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Repdigits as Product of Terms of k-Bonacci Sequences
Mathematics, 2021 For any integer k≥2, the sequence of the k-generalized Fibonacci numbers (or k-bonacci numbers) is defined by the k initial values F−(k−2)(k)=⋯=F0(k)=0 and F1(k)=1 and such that each term afterwards is the sum of the k preceding ones.
Petr Coufal, Pavel Trojovský
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PLoS ONE, 2023 ObjectivesE-cigarettes pose significant risks to youth, but smokers may benefit from switching to e-cigarettes by reducing their exposure to toxicants, which creates a challenge for the Food and Drug Administration (FDA) in regulating e-cigarettes to ...
Yoo Jin Cho +8 more
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