FormalPowerSeries

$$R[[x]]$$

The set of formal power series in the series indeterminate $x$, with coefficients in the ring $R$.

$$R[[x, y]]$$

The set of bivariate formal power series in the series indeterminates $x$ and $y$, with coefficients in the ring $R$.

$$\sum_{n=0}^{\infty} n ! {x}^{n} \in \mathbb{Z}[[x]]$$

Formal power series need not have a nonzero radius of convergence.

$$R[x] \subset R[[x]] \subset R(\!(x)\!) \subset R\!\left\langle\!\left\langle x \right\rangle\!\right\rangle$$

Formal power series generalize polynomials and are generalized by formal Laurent series and formal Puiseux series.

Last updated: 2020-03-06 00:22:16