Results 1 to 10 of about 569 (126)
Some identities of G-continued fractions and generalized continued fractions
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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‘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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Applications in Enumerative Combinatorics of In finite Weighted Automata and Graphs [PDF]
Scientific Annals of Computer Science, 2014 In this paper, we present a general methodology to solve a wide variety of classical lattice path counting problems in a uniform way. These counting problems are related to Dyck paths, Motzkin paths and some generalizations. The methodology uses weighted
R. De Castro, A. Ramírez, J.L. Ramírez
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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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On the convergence of multidimensional S-fractions with independent variables
Karpatsʹkì Matematičnì Publìkacìï, 2020 The paper investigates the convergence problem of a special class of branched continued fractions, i.e. the multidimensional S-fractions with independent variables, consisting of \[\sum_{i_1=1}^N\frac{c_{i(1)}z_{i_1}}{1}{\atop+}\sum_{i_2=1}^{i_1}\frac{c_{
O.S. Bodnar +2 more
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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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Karpatsʹkì Matematičnì Publìkacìï, 2018 The paper deals with research of convergence for one of the generalizations of continued fractions -- branched continued fractions of the special form with two branches.
T.M. Antonova +2 more
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Generalized palindromic continued fractions [PDF]
Rocky Mountain Journal of Mathematics, 2018 11 pages, no figures.
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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 Continued Logarithms and Related Continued Fractions
J. Integer Seq., 2016 We study continued logarithms as introduced by Bill Gosper and studied by J. Borwein et. al.. After providing an overview of the type I and type II generalizations of binary continued logarithms introduced by Borwein et. al., we focus on a new generalization to an arbitrary integer base $b$.
Jonathan M. Borwein +2 more
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