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Re: iterative convolution, discret convolution N times

fd[x_] := Piecewise[{{x + 1, 0 < x < 4}}]

n = 4;

For[i = 1; convn = fd[x], i <= n, i++,
 convn = DiscreteConvolve[convn /. m -> x,
   fd[x], x, m, Assumptions -> m > 0];

NestList[DiscreteConvolve[# /. m -> x,
     fd[x], x, m] &,
   fd[x], n] // Rest // FullSimplify

Bob Hanlon

---- Anna <petitmouton at> wrote: 

HI, I'm trying to do N time convulution of a density funtion called
"fd" with itself . I tried to write an algorithm as shown
For[i = 1; convn = fd, i <= N, i++,
 convn = DiscreteConvolve[convn, fd , x, m, Assumptions -> m > 0];

The initial function fd(x) has x as input variable. After the
convolution, the results convn(m) is in the function of m instead of
x. That's the reason why the algorithm I wrote doesn't work after the
first iteration since the DiscreteConvolve function couldn't find the
input in a function as x anymore.

I would like to ask a question is there a way to change the variable
of a function? for exemple: how can I replace a function y = x+1 by y=m
+1 ???? and is there another way to easily do a convolution N times of
the same function? Thank you very much.
Best regards,

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