[[!redirects inverse series operators]] #Contents# * table of contents {:toc} ## Definition ## Given a [[Z-module|$\mathbb{Z}$-module]] $M$ and a sequence $x:\mathbb{N} \to M$ of terms in $M$, the **inverse series operator** $$\Sigma^{-1}:(\mathbb{N} \to M) \to (\mathbb{N} \to M)$$ is inductively defined as $$\Sigma^{-1}(x)(0) \coloneqq x(0)$$ $$\Sigma^{-1}(x)(i + 1) \coloneqq \Sigma^{-1}(x)(i) - x(i + 1)$$ for $i:\mathbb{N}$. ## See also ## * [[sequence]] * [[series operator]] category: not redirected to nlab yet