Faa di Bruno's formula for Gateaux differentials

Details Faa di Bruno's formula for Gateaux differentials Faa di Bruno's formula for Gateaux differentials

2012-02-01

arxiv.org/abs/1202.0264v1

Mathematics

Functional Analysis

Scientific paper

This paper derives the formula to express higher-order Gateaux differentials
of composite functions in terms of differentials of their factor functions.
This generalises the formula commonly attributed to Italian saint Fa`a di Bruno
to functionals in Banach spaces. The result presented has a simpler and more
general form than previous formulae using partial or ordinary derivatives.

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