On the Divided Difference Form of Faà di Bruno's Formula II (Journal of Computational Mathematics, 2021)
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's formula with a scalar argument. Moreover, a generalized Faà di Bruno's formula with a vector argument is derived.
Keywords: Bell polynomial; Faà di Bruno's formula; Mixed partial divided difference; Multivariate Newton interpolation.