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The multivariate Faà di Bruno formula and multivariate Taylor expansions with explicit integral remainder term

Published online by Cambridge University Press:  17 February 2009

Roy B. Leipnik  and
Charles E. M. Pearce
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Abstract

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The Faà di Bruno formulæ 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 integralform of the remainder term for multivariate Taylor expansions.

Keywords

multivariate composite functionsdifferentiation theoryintegral remainder termmultivariate Taylor seriesFaà di Bruno formula.
Type
Research Article
Information
The ANZIAM Journal , Volume 48 , Issue 3 , January 2007 , pp. 327 - 341
Copyright
Copyright © Australian Mathematical Society 2007

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