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Contents

Idea

A notion of derivative for sequences that behaves as the derivative does for the coefficients of power series.

Definition

Given a $\mathbb{Z}$-module $M$ and a sequence $x:\mathbb{N} \to M$ of terms in $M$, the sequential derivative

is defined as

for $i:\mathbb{N}$.

See also

• sequence
• left shift operator
• sequential antiderivative