Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 59, Issue 6, Pages 2047-2052Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2009.12.009
Keywords
Bell polynomial; Divided difference; Faa di Bruno's formula; Multicomposite function
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Funding
- Education Department of Zhejiang Province of China [Y200806015]
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The well-known formula of Faa di Bruno's for higher derivatives of a composite function has played an important role in combinatorics. In this paper we generalize the divided difference form of Faa di Bruno's formula and give an explicit formula for the n-th divided difference of a multicomposite function. More generally, we establish the relationships of the Bell polynomials with respect to multicomposite functions. Applying these to multicomposite functions, we obtain some extensions of Faa di Bruno's formula. (C) 2009 Elsevier Ltd. All rights reserved.
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