Über eine Verallgemeinerung der Bernoullischen Ungleichung. (On a generalization of Bernoulli's inequality)
type: Item
instance of: scholarly article
title: Über eine Verallgemeinerung der Bernoullischen Ungleichung. (On a generalization of Bernoulli's inequality)
zbMATH Open document ID: 0723.26008
published in: Elemente der Mathematik
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/141481
review text: The author uses MacLaurin's formula \(f(x)=(1+x)^ a- \sum^{k}_{p=0}\binom{a}{p} x^ p\) to prove \textit{L. Gerber}'s inequality [Am. Math. Mon. 75, 875-876 (1968; Zbl 0165.371)]: \[ \binom{a}{k+1}x^{k+1}[(1+x)^ a- \sum^{k}_{p=0} \binom{a}{p} x^ p]\geq 0\text{ for } k\in {\mathbb{N}}\cup \{0\},\;a\in {\mathbb{R}},\;0\neq x>-1. \] \{Since the author expands the expression in square brackets about 0, the definition \(0^ 0:=0\) should be added.\}
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26D10
zbMATH DE Number: 4192049
zbMATH Keywords: Bernoulli inequality
zbMATH Keywords: Gerber inequality
zbMATH Keywords: Taylor's formula
author: Horst Alzer
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4192049