Computation of -partial fractions.
Munagi, Augustine O. (2007)
Integers
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Munagi, Augustine O. (2007)
Integers
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Henry Cohn (1996)
Acta Arithmetica
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Peter J. Grabner, Arnold Knopfmacher (1998)
Mathematica Slovaca
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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.
Komatsu, Takao (2006)
Mathematica Pannonica
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Komatsu, Takao (2004)
Mathematica Pannonica
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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.
Takao Komatsu (2011)
Discussiones Mathematicae - General Algebra and Applications
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Let pₙ/qₙ = [a₀;a₁,...,aₙ] be the n-th convergent of the continued fraction expansion of [a₀;a₁,a₂,...]. Leaping convergents are those of every r-th convergent (n = 0,1,2,...) for fixed integers r and i with r ≥ 2 and i = 0,1,...,r-1. The leaping convergents for the e-type Hurwitz continued fractions have been studied. In special, recurrence relations and explicit forms of such leaping convergents have been treated. In this paper, we consider recurrence relations and explicit forms...
Dominique Barbolosi, Hendrik Jager (1994)
Journal de théorie des nombres de Bordeaux
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Zongduo Dai, Ping Wang, Kunpeng Wang, Xiutao Feng (2007)
Acta Arithmetica
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Bo Li, Yan Zhang, Artur Korniłowicz (2006)
Formalized Mathematics
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The article introduces simple continued fractions. They are defined as an infinite sequence of integers. The characterization of rational numbers in terms of simple continued fractions is shown. We also give definitions of convergents of continued fractions, and several important properties of simple continued fractions and their convergents.
Florin P. Boca, Joseph Vandehey (2012)
Acta Arithmetica
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