Real numbers with polynomial continued fraction expansions
J. Mc Laughlin, Nancy J. Wyshinski (2005)
Acta Arithmetica
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Displaying similar documents to “Corrigendum to the paper 'On the arithmetical theory of continued fractions,II', Acta Arith.7 (1962), pp. 287-298”
Real numbers with polynomial continued fraction expansions
q-Stern Polynomials as Numerators of Continued Fractions
Toufik Mansour (2015)
Bulletin of the Polish Academy of Sciences. Mathematics
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We present a q-analogue for the fact that the nth Stern polynomial Bₙ(t) in the sense of Klavžar, Milutinović and Petr [Adv. Appl. Math. 39 (2007)] is the numerator of a continued fraction of n terms. Moreover, we give a combinatorial interpretation for our q-analogue.
On Hurwitzian and Tasoev's continued fractions
Takao Komatsu (2003)
Acta Arithmetica
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New properties for the Ramanujan-Göllnitz-Gordon continued fraction
Boonrod Yuttanan (2012)
Acta Arithmetica
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A criterion for periodicity of multi-continued fraction expansion of multi-formal Laurent series
Zongduo Dai, Ping Wang, Kunpeng Wang, Xiutao Feng (2007)
Acta Arithmetica
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On certain statistical properties of continued fractions with even and with odd partial quotients
Florin P. Boca, Joseph Vandehey (2012)
Acta Arithmetica
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Non-converging continued fractions related to the Stern diatomic sequence
Boris Adamczewski (2010)
Acta Arithmetica
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Some new families of Tasoevian and Hurwitzian continued fractions
James Mc Laughlin (2008)
Acta Arithmetica
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Polynomial continued fractions
D. Bowman, J. Mc Laughlin (2002)
Acta Arithmetica
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Hurwitz and Tasoev continued fractions with long period.
Komatsu, Takao (2006)
Mathematica Pannonica
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Symmetry and specializability in continued fractions
Henry Cohn (1996)
Acta Arithmetica
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On a theorem of Legendre in the theory of continued fractions
Dominique Barbolosi, Hendrik Jager (1994)
Journal de théorie des nombres de Bordeaux
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On generalization of continued fraction of Gauss.
Denis, Remy Y. (1990)
International Journal of Mathematics and Mathematical Sciences
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On the period of the continued fraction for values of the square root of power sums
Amedeo Scremin (2006)
Acta Arithmetica
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Continued fractions on the Heisenberg group
Anton Lukyanenko, Joseph Vandehey (2015)
Acta Arithmetica
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We provide a generalization of continued fractions to the Heisenberg group. We prove an explicit estimate on the rate of convergence of the infinite continued fraction and several surprising analogs of classical formulas about continued fractions.
Continued fraction expansions for complex numbers-a general approach
S. G. Dani (2015)
Acta Arithmetica
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We introduce a general framework for studying continued fraction expansions for complex numbers, and establish some results on the convergence of the corresponding sequence of convergents. For continued fraction expansions with partial quotients in a discrete subring of ℂ an analogue of the classical Lagrange theorem, characterising quadratic surds as numbers with eventually periodic continued fraction expansions, is proved. Monotonicity and exponential growth are established for the...
Stern Polynomials as Numerators of Continued Fractions
A. Schinzel (2014)
Bulletin of the Polish Academy of Sciences. Mathematics
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It is proved that the nth Stern polynomial Bₙ(t) in the sense of Klavžar, Milutinović and Petr [Adv. Appl. Math. 39 (2007)] is the numerator of a continued fraction of n terms. This generalizes a result of Graham, Knuth and Patashnik concerning the Stern sequence Bₙ(1). As an application, the degree of Bₙ(t) is expressed in terms of the binary expansion of n.