TY - JOUR
T1 - On the Divided Difference Form of Faà di Bruno's Formula II
AU - Xinghua Wang & Aimin Xu
JO - Journal of Computational Mathematics
VL - 6
SP - 697
EP - 704
PY - 2007
DA - 2007/12
SN - 25
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8723.html
KW - Bell polynomial, Faà di Bruno's formula, Mixed partial divided difference,
Multivariate Newton interpolation.
AB - <p style="text-align: justify;">In this paper, we consider the higher divided difference of a composite function $f(g(t))$ in which $g(t)$ is an $s$-dimensional vector. By exploiting some properties from mixed partial divided differences and multivariate Newton interpolation, we generalize the divided difference form of Faà di Bruno&#39;s formula with a scalar argument. Moreover, a generalized Faà di Bruno&#39;s formula with a vector argument is derived.</p>