. C O ] 2 9 A ug 2 00 6 SUFFICIENT CONDITIONS FOR LABELLED 0 – 1 LAWS
نویسنده
چکیده
Exponentiating a power series can have the effect of smoothing out the behavior of the coefficients. In this paper we look at conditions on the growth of the coefficients of G(x) = ∑ g(n)x, where g(n) ≥ 0, which ensure that f(n−1)/f(n)→ ∞, where F(x) = e. Useful notation will be f(n) ≺ g(n) for f(n) eventually less than g(n) and f(n) ∈ RT∞ for f(n− 1)/f(n) → ∞; the notation RT stands for the ratio test. 2. The Coefficients of e
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ar X iv : m at h / 06 08 73 5 v 1 [ m at h . C O ] 2 9 A ug 2 00 6 SUFFICIENT CONDITIONS FOR LABELLED 0 – 1 LAWS
Exponentiating a power series can have the effect of smoothing out the behavior of the coefficients. In this paper we look at conditions on the growth of the coefficients of G(x) = ∑ g(n)x, where g(n) ≥ 0, which ensure that f(n−1)/f(n)→ ∞, where F(x) = e. Useful notation will be f(n) ≺ g(n) for f(n) eventually less than g(n) and f(n) ∈ RT∞ for f(n− 1)/f(n) → ∞; the notation RT stands for the ra...
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