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

Floater, Michael; Lyche, Tom

doi:10.1090/S0025-5718-06-01916-8

Two chain rules for divided differences and Faà di Bruno’s formula
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by Michael S. Floater and Tom Lyche PDF

Math. Comp. 76 (2007), 867-877 Request permission

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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