Results 1 to 10 of about 15,115 (237)
On convergence of generalized continued fractions and Ramanujan's conjecture [PDF]
Comptes Rendus. Mathématique, 2004 We consider continued fractions \frac{-a_1}{1-\frac{a_2}{1-\frac{a_3}{1-...}}} \label{fr} with real coefficients $a_i$ converging to a limit $a$. S.Ramanujan had stated the theorem (see [ABJL], p.38) saying that if $a\neq\frac14$, then the fraction ...
Glutsyuk, A. A.
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Hyperelliptic continued fractions and generalized Jacobians [PDF]
American Journal of Mathematics, 2019 For a complex polynomial $D(t)$ of even degree, one may define the continued fraction of $\sqrt{D(t)}$. This was found relevant already by Abel in 1826, and later by Chebyshev, concerning integration of (hyperelliptic) differentials; they realized that, contrary to the classical case of square roots of positive integers treated by Lagrange and Galois ...
Capuano, Laura +3 more
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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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Generalized continued fraction expansions for π and e
Journal of Discrete Mathematical Sciences and Cryptography, 2021 Recently Raayoni et al. announced various conjectures on continued fractions of fundamental constants automatically generated with machine learning techniques. In this paper we prove some of their stated conjectures for Euler number $e$ and show the equivalence of some of the listed conjectures.
Mashurov, Farukh, Kadyrov, Shirali
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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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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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The Generating Function of Ternary Trees and Continued Fractions [PDF]
The Electronic Journal of Combinatorics, 2006 Michael Somos conjectured a relation between Hankel determinants whose entries ${1\over 2n+1}{3n\choose n}$ count ternary trees and the number of certain plane partitions and alternating sign matrices. Tamm evaluated these determinants by showing that the generating function for these entries has a continued fraction that is a special case of Gauss's ...
Gessel, Ira M., Xin, Guoce
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From asymptotics to spectral measures: determinate versus indeterminate moment problems [PDF]
, 2005 In the field of orthogonal polynomials theory, the classical Markov theorem shows that for determinate moment problems the spectral measure is under control of the polynomials asymptotics.
Valent, Galliano
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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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