Re: iterative convolution, discret convolution N times

*To*: mathgroup at smc.vnet.net*Subject*: [mg102458] Re: [mg102424] iterative convolution, discret convolution N times*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Sun, 9 Aug 2009 18:22:12 -0400 (EDT)*Reply-to*: hanlonr at cox.net

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]; Print[FullSimplify[convn]]] NestList[DiscreteConvolve[# /. m -> x, fd[x], x, m] &, fd[x], n] // Rest // FullSimplify Bob Hanlon ---- Anna <petitmouton at gmail.com> 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]; Print[convn]] 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, Victoria