Relationships between classes of monotonic functions
نویسندگان
چکیده
منابع مشابه
Some Classes of Completely Monotonic Functions
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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A function f : (0,∞) → R is said to be completely monotonic if (−1)nf (n)(x) ≥ 0 for all x > 0 and n = 0, 1, 2, .... In this paper we present several new classes of completely monotonic functions. Our functions have in common that they are defined in terms of the classical gamma, digamma, and polygamma functions. Moreover, we apply one of our monotonicity theorems to prove a new inequality for ...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1976
ISSN: 0304-3975
DOI: 10.1016/0304-3975(76)90034-7