The multivariate Faà di Bruno formula and multivariate Taylor expansions with explicit integral remainder term
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AbstractThe 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.
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1995 ◽
Vol 5
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pp. 1-35
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2017 ◽
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pp. 1820-1842
1999 ◽
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pp. 121-128
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2007 ◽
Vol 424
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pp. 240-281
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