Results 41 to 50 of about 5,022,265 (207)
The Generating Functions for Special Pringsheim Continued Fractions
Communications in Advanced Mathematical Sciences, 2020 In previous works, some relations between Pringsheim continued fractions and vertices of the paths of minimal length on the suborbital graphs $\mathrm{\mathbf{F}}_{u,N}$ were investigated.
Ali Hikmet Değer, Ümmügülsün Akbaba
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The relative growth rate for partial quotients in continued fractions
Journal of Mathematical Analysis and Applications, 2019 For an irrational number x ∈ [ 0 , 1 ) , let x = [ a 1 ( x ) , a 2 ( x ) , … ] be its continued fraction expansion and { p n ( x ) q n ( x ) , n ≥ 1 } be the sequence of rational convergents.
Bo Tan, Qinglong Zhou
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Hyperelliptic continued fractions and generalized Jacobians [PDF]
American Journal of Mathematics, 2016 :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 then by Chebyshev, concerning integration of (hyperelliptic) differentials; they realized that ...
U. Zannier
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On the metrical theory of a non-regular continued fraction expansion
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2015 We introduced a new continued fraction expansions in our previous paper. For these expansions, we show the Brodén-Borel-Lévy type formula. Furthermore, we compute the transition probability function from this and the symbolic dynamical system of the ...
Lascu Dan, Cîrlig George
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Planar maps and continued fractions
, 2011 We present an unexpected connection between two map enumeration problems. The first one consists in counting planar maps with a boundary of prescribed length. The second one consists in counting planar maps with two points at a prescribed distance.
BenderE.A. +15 more
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Continued fractions related to a group of linear fractional transformations
Open Mathematics, 2023 There are strong relations between the theory of continued fractions and groups of linear fractional transformations. We consider the group G3,3{G}_{3,3} generated by the linear fractional transformations a=1−1∕za=1-1/z and b=z+2b=z+2.
Demir Bilal
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Convergence criterion for branched contіnued fractions of the special form with positive elements
Karpatsʹkì Matematičnì Publìkacìï, 2017 In this paper the problem of convergence of the important type of a multidimensional generalization of continued fractions, the branched continued fractions with independent variables, is considered.
D.I. Bodnar, I.B. Bilanyk
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Tasoev's continued fractions and Rogers–Ramanujan continued fractions
Journal of Number Theory, 2004 The author of this paper discusses Tasoev's continued fractions, which are of the form \[ [0;\underbrace{a,\dots,a}_m,\underbrace{a^2,\dots,a^2}_m, \dots]\equiv[0;\underbrace{\overline{a^k,\dots,a^k}}_m]_{k=1}^\infty,\;(m\geq1), \] and for a modified form he proves that \[ [0;\overline{ua^{2k-1}-1,1,va^{2k}-1}]_{k=1}^\infty=\frac{\sum_{s=0}^\infty u ...
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Continued Fractions of Square Roots of Natural Numbers
Acta Polytechnica, 2013 In this paper, we will first summarize known results concerning continued fractions. Then we will limit our consideration to continued fractions of quadratic numbers.
L'ubomíra Balková, Aranka Hrušková
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Continued fractions of certain Mahler functions
, 2018 We investigate the continued fraction expansion of the infinite products $g(x) = x^{-1}\prod_{t=0}^\infty P(x^{-d^t})$ where polynomials $P(x)$ satisfy $P(0)=1$ and $\deg(P)1$ such that $g(b)\neq0$ the irrationality exponent of $g(b)$ equals two.
Badziahin, Dmitry
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