منابع مشابه
Some Linear and Some Quadratic Recursion Formulas
§ 1. Introduction We shall mainly deal with linear recursion formulas of the type n-1 (l. 1) f(1) = 1 ; /(n) _ i~ ck f(n-k) (n = 2, 3,. . .), k=1 and with quadratic formulas of the type n-1 (1. 2) f(1) = 1 ; /(n) _ d, f(k)/(n-k) (n = 2,3. . .). k=1 We assume that ck > 0, d k > 0 (k = 1, 2,. . .). In a previous paper [1] we discussed (1. 1) under the condition X° ck = 1, and further special assu...
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A new selection is made of the most practical of the many explicit Runge-Kutta formulas of order 4 which have been proposed. A new formula is considered, formulas are modified to improve their quality and efficiency in agreement with improved understanding of the issues, and formulas are derived which permit interpolation. It is possible to do a lot better than the pair of Fehlberg currently re...
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We show how to find series expansions for π of the form π = ∞ n=0 S(n) mn pn a n , where S(n) is some polynomial in n (depending on m, p, a). We prove that there exist such expansions for m = 8k, p = 4k, a = (−4) k , for any k, and give explicit examples for such expansions for small values of m, p and a.
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We show that, up to renaming of the letters, the only infinite ternary words avoiding the formulaABCAB.ABCBA.ACB.BAC (resp. ABCA.BCAB.BCB.CBA) have the same set of recurrent factors as the fixed point of 0 7→ 012, 1 7→ 02, 2 7→ 1. Also, we show that the formula ABAC.BACA.ABCA is 2-avoidable. Finally, we show that the pattern ABACADABCA is unavoidable for the class of C4-minor-free graphs with m...
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ژورنال
عنوان ژورنال: Tohoku Mathematical Journal
سال: 1954
ISSN: 0040-8735
DOI: 10.2748/tmj/1178245173