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A new algorithm for computing the multivariate Faà di Bruno’s formula |
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| Authors: | E Di Nardo G Guarino |
| Institution: | a Dipartimento di Matematica e Informatica, Università degli Studi della Basilicata, Viale dell’Ateneo Lucano 10, 85100 Potenza, Italy b Medical School, Università Cattolica del Sacro Cuore (Rome branch), Largo Agostino Gemelli 8, I-00168 Roma, Italy |
| 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. |
| Keywords: | Multivariate composite function Faà di Bruno&rsquo s formula Multivariate cumulant Multivariate Hermite polynomial Classical umbral calculus |
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