Displaying similar documents to “Some infinite products with interesting continued fraction expansions”

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.

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.

Leaping convergents of Hurwitz continued fractions

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 p r n + i / q r n + i (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...

Simple Continued Fractions and Their Convergents

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.