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Re: RSolve problem: won't solve convolution recurrence relation.

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  • Subject: [mg106252] Re: RSolve problem: won't solve convolution recurrence relation.
  • From: dh <dh at>
  • Date: Wed, 6 Jan 2010 06:00:15 -0500 (EST)
  • References: <hhuna6$nil$>

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],


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 



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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