Faa di Bruno's formula for chain differentials

Abstract

This paper determines the general formula for describing differentials of composite functions in terms of differentials of their factor functions. This generalises the formula commonly attributed to Faa di Bruno to functions in locally convex topological vector spaces. The result highlights the general structure of the higher-order chain rule in terms of partitions of the directions.

arXiv admin note: substantial text overlap with arXiv:1202.0264

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