Exchangeable events and completely monotonic sequences
نویسندگان
چکیده
منابع مشابه
On the Composition of Completely Monotonic Functions and Completely Monotonic Sequences and Related Questions
If, in addition, f(x) is continuous at x = a, then it is called completely monotonic over [a, b), with similar definitions for (a, b] and [a, b]. A function is absolutely monotonic if all its derivatives are non-negative. A detailed study of these concepts can be found, for example, in [11, Chapter IV]. Our chief concern here is for the standard case in which a = 0, b = + 00. For this, S. N. Be...
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*Correspondence: [email protected] 1Department of Mathematics, Zhongyuan University of Technology, Zhengzhou, Henan 450007, People’s Republic of China Full list of author information is available at the end of the article Abstract In this article, we present some necessary conditions, a sufficient condition and a necessary and sufficient condition for sequences to be completely monotonic. One co...
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We prove: (i) Let Fn(x) = Pn(x) [ e− ( 1 + 1 x )x] and Gn(x) = Pn(x) [( 1 + 1 x )x+1 − e ] , where Pn(x) = xn + ∑n−1 ν=0 cνx ν is a polynomial of degree n ≥ 1 with real coefficients. Fn is completely monotonic if and only if n = 1 and c0 ≥ 11/12; and Gn is completely monotonic if and only if n = 1 and c0 ≥ 1/12. (ii) The functions x 7→ e − (1 + 1/x)x and x 7→ (1 + 1/x)x+1 − e are Stieltjes tran...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1973
ISSN: 0035-7596
DOI: 10.1216/rmj-1973-3-4-565