Homogeneous interpolation and some continued fractions
نویسندگان
چکیده
منابع مشابه
Homogeneous 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.
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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...
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We derive closed-form expressions for several new classes of Hurwitzianand Tasoevian continued fractions, including [0; p− 1, 1, u(a + 2nb)− 1, p− 1, 1, v(a + (2n + 1)b)− 1 ]n=0, [0; c + dmn]n=1 and [0; eun, fvn] ∞ n=1. One of the constructions used to produce some of these continued fractions can be iterated to produce both Hurwitzianand Tasoevian continued fractions of arbitrary long quasi-pe...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society, Series B
سال: 2014
ISSN: 2330-0000
DOI: 10.1090/s2330-0000-2014-00001-0