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Convolution

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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.


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