# Convolution of a function with itself

#### mhill

given a function f(t) could we define the operation

$$f*f*f*f*f*f*f*f**f*f*f*f*..........*f$$ n times ?

here the operation '*' means convolution of a function if n=2 i know the expression

$$(f*f)= \int_{0}^{x}dt f(t)f(t-x)$$

but i would like to see if this can be applied to arbitrary order , thanks.

#### mathman

Science Advisor
given a function f(t) could we define the operation

$$f*f*f*f*f*f*f*f**f*f*f*f*..........*f$$ n times ?

here the operation '*' means convolution of a function if n=2 i know the expression

$$(f*f)= \int_{0}^{x}dt f(t)f(t-x)$$

but i would like to see if this can be applied to arbitrary order , thanks.
There is nothing in mathematics to prevent you from doing it.

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