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Multivariate Bell Polynomials and Derivatives of Composed Functions · Around

2019

Multivariate Bell Polynomials and Derivatives of Composed Functions

Schumann, Aidan

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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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Bell, E.T.:
1934
Earlier work this paper cites.
Riordan, J.:
1946
Earlier work this paper cites.
Constantine, G. & Savits, T.:
1996
Earlier work this paper cites.
Mishkov, R.L.:
2000
Earlier work this paper cites.
Charalambides, C.A.:
2002
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