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Volume 25, Issue 6
On the Divided Difference Form of Faà di Bruno's Formula II

Xinghua Wang & Aimin Xu

J. Comp. Math., 25 (2007), pp. 697-704.

Published online: 2007-12

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  • Abstract

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.

  • AMS Subject Headings

65D05, 05A10, 41A05.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-25-697, author = {Xinghua Wang and Aimin Xu}, title = {On the Divided Difference Form of Faà di Bruno's Formula II}, journal = {Journal of Computational Mathematics}, year = {2007}, volume = {25}, number = {6}, pages = {697--704}, abstract = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8723.html} }
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 -

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.

Xinghua Wang and Aimin Xu. (2007). On the Divided Difference Form of Faà di Bruno's Formula II. Journal of Computational Mathematics. 25 (6). 697-704. doi:
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