How to Easily Convolve a Function with Itself?

[thomitsu]

Hallo there!

I was wondering wether there is an easy way to convolve a function with itself.
For example is ther an easy formula or something that gives directly the result?
thanks in advance

 

[thomitsu]

for example, for correlation...

The correlation of a function with itself is called its autocorrelation
In this case the correlation theorem becomes
the transform pair
– This is the Wiener-Khinchin Theorem
Corr(g,g)↔G( f )G*( f ) = G( f )^2

Is there something like that for convolution?

 

[mathman]

I don't know if it helps any, but take the Fourier transform of the function, square the transform, and take the inverse transform of the result.

 

[thomitsu]

Oh god! This is so complicated( my function is a squared bessel function)! I will try it though.thank you so much!