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Re: RSolve problem: won't solve convolution recurrence relation.
*To*: mathgroup at smc.vnet.net
*Subject*: [mg106252] Re: RSolve problem: won't solve convolution recurrence relation.
*From*: dh <dh at metrohm.com>
*Date*: Wed, 6 Jan 2010 06:00:15 -0500 (EST)
*References*: <hhuna6$nil$1@smc.vnet.net>
Hi Sam,
in fact, Mathematica can solve your equation. Straight from the manual:
Nonlinear convolution equation:
RSolve[{a[n + 1] == Sum[a[m] a[n - m], {m, 0, n}], a[0] == 1}, a[n],
n]
Note that counting starts at zero here.
However, Mathematica fails if you start counting from 1 instead of 0:
RSolve[{a[n + 1] == Sum[a[m] a[n - m + 1], {m, 1, n}], a[1] == 1},
a[n], n]
this produces your error message.
I think this is a bug in inpout section of RSolve. Please report this to
Wolfram.
Daniel
Sam wrote:
> I am using mathematica 7, and am trying to solve a recurrence relation
> using the code below:
>
> RSolve[{f[x] == Sum[f[i]*f[x - i], {i, 1, x - 1}], f[1] == 1}, f[x],
> x]
>
> but it gives me the RSolve::piarg error. I have found that the
> solution for the above problem is in fact
>
> f[x_] = Product[(4*i - 6)/i, {i, 2, x}]
>
> so it is theoretically solveable, but doing this sort of thing by hand
> is extremely error prone. Is there any way of solving this type of
> problem with mathematica or is it necessary to do it by hand?
>
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