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

Roy B. Leipnik, Charles E.M. Pearce

• 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.