A new algorithm for computing the multivariate Faà di Bruno's formula

Abstract

A new algorithm for computing the multivariate Faà di Bruno's formula is provided. We use a symbolic approach based on the classical umbral calculus that turns the computation of the multivariate Faà di Bruno's formula into a suitable multinomial expansion. We propose a MAPLE procedure whose computational times are faster compared with the ones existing in the literature. Some illustrative applications are also provided.

The procedure in MAPLE for computing the multivariate Faà di Bruno's formula is given in the Appendix 1 of the paper

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