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

• Autores: Roy B. Leipnik, Charles E.M. Pearce
• Localización: Anziam journal: The Australian & New Zealand industrial and applied mahtematics journal, ISSN 1446-1811, Vol. 48, Nº 3, 2007, págs. 327-341
• Idioma: inglés
• DOI: 10.1017/s1446181100003527
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• Resumen

  • 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.