The Faà di Bruno formula and determinant identities
✍ Scribed by Wenchang *, Chu
- Book ID
- 121084619
- Publisher
- Taylor and Francis Group
- Year
- 2006
- Tongue
- English
- Weight
- 222 KB
- Volume
- 54
- Category
- Article
- ISSN
- 0308-1087
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📜 SIMILAR VOLUMES
Some years ago Gessel ([Ge]) introduced a q-analogue of functional composition that was strong enough to support a q-analogue of the chain rule. In this note we show that Gessel's q-composition is even strong enough to support a q-analogue of FaaÁ di Bruno's formula for the n th derivative of a comp
A short proof-of the generalized F& di Bruno formula is given and an explicit parametrization of the set of indices involved in the coefficient of a specific term of the formula is provided. An application is also included.
## a b s t r a c t The well-known formula of Faà 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 Faà di Bruno's formula and give an explicit formula for the n-th divided difference of