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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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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).
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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.
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Pringsheim's theorem for generalized continued fractions
Journal of Computational and Applied Mathematics, 1986 A theorem on the convergence of generalized continued fractions is presented. The result achieved represents an interesting generalization of a well-known theorem due to Pringsheim.
Paul Levrie
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Generalized palindromic continued fractions [PDF]
Rocky Mountain Journal of Mathematics, 2018 11 pages, no figures.
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Description of Generalized Continued Fractions by Finite Automata [PDF]
, 2013 A generalized continued fraction algorithm associates with every real number x a sequence of integers; x is rational iff the sequence is finite. For a fixed algorithm, call a sequence of integers valid if it is the result of that algorithm on some input ...
C. Brezinski +11 more
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On Salem numbers, expansive polynomials and Stieltjes continued fractions [PDF]
, 2014 A converse method to the Construction of Salem (1945) of convergent families of Salem numbers is investigated in terms of an association between Salem polynomials and Hurwitz quotients via expansive polynomials of small Mahler measure.
Guichard, Christelle +1 more
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Continued-Fraction Expansion of Transport Coefficients with Fractional Calculus
Mathematics, 2016 The main objective of this paper is to generalize the Extended Irreversible Thermodynamics in order to include the anomalous transport in systems in non-equilibrium conditions.
Abel Garcia-Bernabé +3 more
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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
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General convergence of continued fractions [PDF]
Transactions of the American Mathematical Society, 1986 We introduce a new concept of convergence of continued fractions—general convergence. Moreover, we compare it to the ordinary convergence concept and to strong convergence. Finally, we prove some properties of general convergence.
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