Convolution

From AoPSWiki

The convolution of two functions can mean various things.

In number theoretic context, convolution of two functions $f,g : \mathbb{N} \rightarrow \mathbb{C}$ usually means Dirichlet convolution, defined as $\displaystyle f * g = \sum_{d\mid n} f(d)g\left( \frac{n}{d} \right)$ .

In analytic context, convolution of functions $\displaystyle f, g$ usually means a function of the form $\int f(\tau) g(t-\tau) d\tau$ .

This article is a stub. Help us out by expanding it.

Personal tools

Navigation

Search

Toolbox

Convolution

From AoPSWiki