Taylor expansions of the exponential exp(x), natural logarithm ln(1+x), and binomial series (1+x)n are derived to low order without using calculus. It is particularly simple to develop and graph the expansions to linear power in x. An example is presented of the application of the first...
a基于这个原理,文中对重要函数 e 的极限式、Taylor展开式、Pade有理逼近引入了非线性展开和逼近的讨论,给出了这些函数的非线性Taylor展开、非线性Pade有理逼近等多个推广式。 Based on this principle, in the article to the importance function e limit type, the Taylor expansion, Pade rational approximatio...
Various approximate solutions based on Taylor series expansions have been proposed [9], =-=[8]-=-, [5]. Newman [16] introduces a statistical approximation based on exciting the system with white Gaussian noise and then computing the balancing transformation using an algorithm from differential to...
The Important State Coordinates of a Nonlinear System - Krener - 2007 () Citation Context ...te the coordinate change x = 蠒(z), however there are no systematic methods or tools for solving these problems. Various approximate solutions based on Taylor series expansions have been proposed [9]...
Expansions of the Elementary FunctionsGeometrical ApplicationsExample of a Function which Cannot be Expanded in a Taylor SeriesProof That e is IrrationalProof That the Binomial Series ConvergesZeros and Infinities of Functions, and So-Called Indeterminate Expressions...
Huntington’s disease (HD) is an autosomal dominantly inherited neurodegenerative condition characterized by CAG-triplet expansions within the huntingtin gene (HTT) resulting in a polyglutamine stretch in the HTT protein. There are plenty of studies assessing the role of the KP in HD. In the early...