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arXiv · 1903.03899

Multivariate Bell Polynomials and Derivatives of Composed Functions

Aidan Schumann
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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 $\textbf{f}(\textbf{g}(\textbf{x}))$.

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Aidan Schumann. 2019-03-10. Multivariate Bell Polynomials and Derivatives of Composed Functions. https://arxiv.org/abs/1903.03899

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