Bracket notation for the `coefficient of' operator
| dc.creator | Knuth, Donald E. | |
| dc.date | 1994-02-23 | |
| dc.date.accessioned | 2026-07-07T09:15:04Z | |
| dc.date.available | 2026-07-07T09:15:04Z | |
| dc.description | When $G(z)$ is a power series in $z$, many authors now write `$[z^n] G(z)$' for the coefficient of $z^n$ in $G(z)$, using a notation introduced by Goulden and Jackson in [\GJ, p. 1]. More controversial, however, is the proposal of the same authors [\GJ, p. 160] to let `$[z^n/n!] G(z)$' denote the coefficient of $z^n/n!$, i.e., $n!$ times the coefficient of $z^n$. An alternative generalization of $[z^n] G(z)$, in which we define $[F(z)] G(z)$ to be a linear function of both $F$ and $G$, seems to be more useful because it facilitates algebraic manipulations. The purpose of this paper is to explore some of the properties of such a definition. The remarks are dedicated to Tony Hoare because of his lifelong interest in the improvement of notations that facilitate manipulation. | |
| dc.identifier | https://arxiv.org/abs/math/9402216 | |
| dc.identifier | http://arxiv.org/abs/math/9402216 | |
| dc.identifier | A Classical Mind, essays in honour of C. A. R. Hoare, 1994 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152895 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.title | Bracket notation for the `coefficient of' operator | |
| dc.type | text |