Results 11 to 20 of about 15,074 (239)
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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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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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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Path generating functions and continued fractions
Journal of Combinatorial Theory, Series A, 1986 From the authors' abstract: ``This paper extends \textit{P. Flajolet}'s [Discrete Math. 32, 125--161 (1980; Zbl 0445.05014)] combinatorial theory of continued fractions by obtaining the generating function for paths between horizontal lines, with arbitrary starting and ending point and weights on the steps.
Goulden, I.P, Jackson, D.M
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Generalized Brouncker’s continued fractions and their logarithmic derivatives [PDF]
The Ramanujan Journal, 2013 In this paper, we study the continued fraction y(s,r) which satisfies the equation y(s,r)y(s+2r,r)=(s+1)(s+2r-1) for r > 1/2. This continued fraction is a generalization of the Brouncker's continued fraction b(s). We extend the formulas for the first and the second logarithmic derivatives of b(s) to the case of y(s,r).
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Generalized Continued Logarithms and Related Continued Fractions
, 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 $b$.
Borwein, Jonathan M. +2 more
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The quantum chaos conjecture and generalized continued fractions [PDF]
Sbornik: Mathematics, 2003 Summary: The proof of the quantum chaos conjecture is given for a class of systems including as a special case the model of a rotating particle under the action of periodic impulse perturbations. (The distribution of the distances between adjacent energy levels is close to the Poisson distribution and differs from it by terms of the third order of ...
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Continuous time random walk and diffusion with generalized fractional Poisson process [PDF]
Physica A: Statistical Mechanics and its Applications, 2020 27 pages, 4 figures. Accepted for publication in Physica A.
Michelitsch, Thomas, Riascos, Alejandro
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Continued Fraction Expansion of Fluctuation Spectrum and Generalized Time Correlation [PDF]
Progress of Theoretical Physics, 1987 A practical approximation method for the fluctuation spectrum and generalized time correlation for a time series observed in stochastic or chaotic dynamics is proposed by utilizing the continued fraction expansion. The present approach enables us to evaluate the fluctuation spectrum and generalized time correlation in a systematic way without trying to
Hirokazu Fujisaka, Masayoshi Inoue
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