Why do partitions occur in Faa di Bruno's chain rule for higher derivatives?
General Mathematics
2007-05-23 v1 Functional Analysis
Abstract
It is well-known that the coefficients in Faa di Bruno's chain rule for higher derivatives can be expressed via numeration of partitions. It turns out that this has a natural form as a formula for the vector case. To this formula two proofs are presented, both "explaining" its form involving partitions: one as a purely algebraic fact, and one "from first principles" for the case of Frechet derivatives of mappings between Banach spaces.
Keywords
Cite
@article{arxiv.math/0602183,
title = {Why do partitions occur in Faa di Bruno's chain rule for higher derivatives?},
author = {Eliahu Levy},
journal= {arXiv preprint arXiv:math/0602183},
year = {2007}
}
Comments
10 pages