Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/44162
Type: | Journal article |
Title: | The multivariate Faa di Bruno formula and multivariate Taylor expansions with explicit integral remainder term |
Author: | Leipnik, R. Pearce, C. |
Citation: | Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal, 2007; 48:327-341 |
Publisher: | Australian Mathematical Society |
Issue Date: | 2007 |
ISSN: | 1446-1811 |
Statement of Responsibility: | Roy B. Leipnik and Charles E. M. Pearce |
Abstract: | The Faà di Bruno formulae for higher-order derivatives of a composite function are important in analysis for a variety of applications. There is a substantial literature on the univariate case, but despite significant applications the multivariate case has until recently received limited study. We present a succinct result which is a natural generalization of the univariate version. The derivation makes use of an explicit integral form of the remainder term for multivariate Taylor expansions. |
Description: | Copyright © Australian Mathematical Society This paper is made available with the permission of the Australian Mathematical Society Inc. |
Published version: | http://www.austms.org.au/Publ/Jamsb/V48P3/2528.html |
Appears in Collections: | Aurora harvest 6 Mathematical Sciences publications |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
hdl_44162.pdf | 146.97 kB | Publisher's PDF | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.