منابع مشابه
Some More Long Continued Fractions, I
In this paper we show how to construct several infinite families of polynomials D(x̄, k), such that p D(x̄, k) has a regular continued fraction expansion with arbitrarily long period, the length of this period being controlled by the positive integer parameter k. We also describe how to quickly compute the fundamental units in the corresponding real quadratic fields.
متن کاملSingularity of Some Random Continued Fractions
We prove singularity of some distributions of random continued fractions that correspond to iterated function systems with overlap and a parabolic point. These arose while studying the conductance of GaltonWatson trees. §
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Recently, Bergman [2] provided an explicit, nonrecursive description of the partial quotients in (1), and by implication, in (2). (This description is our Theorem 3.) The purpose of this paper is to prove Bergman's result, and to provide similar results for the continued fractions given in [3] and [4]. We start off with some terminology about "strings." By a string9 we mean a (finite or infinit...
متن کاملHomogeneous Interpolation and Some Continued Fractions
We prove: if d/m < 2280/721, there is no curve of degree d passing through n = 10 general points with multiplicity m in P. Similar results are given for other special values of n. Our bounds can be naturally written as certain palindromic continued fractions.
متن کاملSome aspects of multidimensional continued fraction algorithms
Many kinds of algorithms of continued fraction expansions of dimension s(≥ 2) have been studied starting with K.G.J.Jacobi(1804-1851), for example, see [14]. For s = 1, we know Lagrange’s theorem related to periodic continued fractions and real quadratic irrationals. But, even for real cubic irrationalities, there appeared no suitable algorithms (of dimension 2). In this section, we roughly exp...
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ژورنال
عنوان ژورنال: The Musical Times
سال: 1914
ISSN: 0027-4666
DOI: 10.2307/906928