منابع مشابه
Infinite Series
so π is an “infinite sum” of fractions. Decimal expansions like this show that an infinite series is not a paradoxical idea, although it may not be clear how to deal with non-decimal infinite series like (1.1) at the moment. Infinite series provide two conceptual insights into the nature of the basic functions met in high school (rational functions, trigonometric and inverse trigonometric funct...
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In this paper a new direct proof for the irrationality of Euler's number e = ∞ k=0 1 k! is presented. Furthermore, formulas for the base b digits are given which, however, are not computably effective. Finally we generalize our method and give a simple criterium for some fast converging series representing irrational numbers.
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Motivated by a conjecture of Ellentuck concerning fibers f^x(C), f recursive and C an element of one of Barback's "tame models" (Tame models in the isols, Houston J. Math. 12 (1986), 163-175), we study such fibers in the more general context of Nerode semirings. The principal results are that (1) all existentially complete Nerode semirings meet all of their recursive fibers, and (2) not all Ner...
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It reviews the theory of Hidden Filter Hidden Markov Models and presents an extension, Mixed State Hidden Markov Models, developed jointly by Andrew Fraser and myself under his supervision. This manuscript version has only trivial differences from the original.
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In the present paper we investigate the following problems. Suppose an >O for n_-I and Z a,=-. n=1 N° 1. Does there exist a sequence of natural numbers No =O, Ni l-, such that it decomposes the series monotone decreasingly : In order to state the second problem we define the index nk (c) as the minimum m such that (2) Now the second problem is as follows. are equiconvergent. m kc a j. j=1 N° 2....
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ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 1973
ISSN: 0029-4527
DOI: 10.1305/ndjfl/1093891104