Multivariate Bell Polynomials and Derivatives of Composed Functions
Classical Analysis and ODEs
2019-03-12 v1
Abstract
How do we take repeated derivatives of composed multivariate functions? for one-dimensional functions, the common tools consist of the Fa\'a di Bruno formula with Bell polynomials; while there are extensions of the Fa\'a di Bruno formula, there are no corresponding Bell polynomials. In this paper, we generalize the single-variable Bell polynomials to take vector-valued arguments indexed by multi-indices which we use to rewrite the Fa\'a di Bruno formula to find derivatives of .
Cite
@article{arxiv.1903.03899,
title = {Multivariate Bell Polynomials and Derivatives of Composed Functions},
author = {Aidan Schumann},
journal= {arXiv preprint arXiv:1903.03899},
year = {2019}
}
Comments
16 pages, 2 tables