Homotopy Type Theory inverse series operator > history (Rev #2, changes)

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Definition

Given a $\mathbb{Z}$-module MM and a sequence x:Mx:\mathbb{N} \to M of terms in MM, the inverse series operator

Σ 1:(M)(M)\Sigma^{-1}:(\mathbb{N} \to M) \to (\mathbb{N} \to M)

is inductively defined as

Σ 1(x)(0)x(0)\Sigma^{-1}(x)(0) \coloneqq x(0)
Σ 1(x)(i+1)Σ 1(x)(i)x(i+1)\Sigma^{-1}(x)(i + 1) \coloneqq \Sigma^{-1}(x)(i) - x(i + 1)

for i:i:\mathbb{N}.

See also

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