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Two chain rules for divided differences and Faà di Bruno's formula

Authors: Michael S. Floater and Tom Lyche
Journal: Math. Comp. 76 (2007), 867-877
MSC (2000): Primary 05A17, 05A18, 26A06, 26A24, 41A05, 65D05
Published electronically: October 30, 2006
MathSciNet review: 2291840
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we derive two formulas for divided differences of a function of a function. Both formulas lead to other divided difference formulas, such as reciprocal and quotient rules. The two formulas can also be used to derive Faà di Bruno's formula and other formulas for higher derivatives of composite functions. We also derive a divided difference version of Faà di Bruno's determinant formula.

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Additional Information

Michael S. Floater
Affiliation: Centre of Mathematics for Applications, Department of Informatics, University of Oslo, PO Box 1053, Blindern, 0316 Oslo, Norway

Tom Lyche
Affiliation: Centre of Mathematics for Applications, Department of Informatics, University of Oslo, PO Box 1053, Blindern, 0316 Oslo, Norway

Keywords: Chain rule, divided differences, Fa{\`a} di Bruno's formula.
Received by editor(s): July 20, 2005
Published electronically: October 30, 2006
Article copyright: © Copyright 2006 American Mathematical Society

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