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Aq-Analogue of Faà di Bruno's Formula

✍ Scribed by Warren P. Johnson

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
285 KB
Volume
76
Category
Article
ISSN
0097-3165

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✦ Synopsis

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 composite function. q-analogues of the Bell polynomials arise naturally in this context. 1996 Academic Press, Inc.

I. ELEMENTARY q-DIFFERENTIAL CALCULUS

We will use a well-known q-analogue of the derivative operator that goes back at least to Jackson [Ja]. Related operators were used earlier by Heine and by Rogers; see also [An2], [GR]. We define _ n k 1 , k 2 , ..., k m & = n! q (k 1 )! q (k 2 )! q } } } (k m )! q article no.

📜 SIMILAR VOLUMES

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