The Complete Monotonicity of a Function Studied by Miller and Moskowitz

Alzer, Horst. "The Complete Monotonicity of a Function Studied by Miller and Moskowitz." Bollettino dell'Unione Matematica Italiana 2.2 (2009): 449-452. <http://eudml.org/doc/290567>.

@article{Alzer2009,
abstract = {Let $$S(x) = log(1+x) + \int\_\{0\}^\{1\} \left[ 1 - \left( \frac\{1+t\}\{2\} \right) ^\{x\} \right] \frac\{dt\}\{\log t\} \quad \text\{and\} \quad F(x) = \log 2 - S(x) \,\, (0 < x \in \mathbb\{R\}).$$ We prove that $F$ is completely monotonic on $(0,\infty)$. This complements a result of Miller and Moskowitz (2006), who proved that $F$ is positive and strictly decreasing on $(0,\infty)$. The sequence $\\{ S(k)\\}$$(k=1,2,\dots)$ plays a role in information theory.},
author = {Alzer, Horst},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {449-452},
publisher = {Unione Matematica Italiana},
title = {The Complete Monotonicity of a Function Studied by Miller and Moskowitz},
url = {http://eudml.org/doc/290567},
volume = {2},
year = {2009},
}

TY - JOUR
AU - Alzer, Horst
TI - The Complete Monotonicity of a Function Studied by Miller and Moskowitz
JO - Bollettino dell'Unione Matematica Italiana
DA - 2009/6//
PB - Unione Matematica Italiana
VL - 2
IS - 2
SP - 449
EP - 452
AB - Let $$S(x) = log(1+x) + \int_{0}^{1} \left[ 1 - \left( \frac{1+t}{2} \right) ^{x} \right] \frac{dt}{\log t} \quad \text{and} \quad F(x) = \log 2 - S(x) \,\, (0 < x \in \mathbb{R}).$$ We prove that $F$ is completely monotonic on $(0,\infty)$. This complements a result of Miller and Moskowitz (2006), who proved that $F$ is positive and strictly decreasing on $(0,\infty)$. The sequence $\{ S(k)\}$$(k=1,2,\dots)$ plays a role in information theory.
LA - eng
UR - http://eudml.org/doc/290567
ER -