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Re: RSolve problem: won't solve convolution recurrence
*To*: mathgroup at smc.vnet.net
*Subject*: [mg106254] Re: [mg106224] RSolve problem: won't solve convolution recurrence
*From*: DrMajorBob <btreat1 at austin.rr.com>
*Date*: Wed, 6 Jan 2010 06:00:39 -0500 (EST)
*References*: <201001050648.BAA24170@smc.vnet.net>
*Reply-to*: drmajorbob at yahoo.com
This works:
Clear[f]
f[1] = 1;
f[x_Integer?Positive] := f[x] = Sum[f[i]*f[x - i], {i, 1, x - 1}]
g = FindSequenceFunction@Array[f, 6]
(4^(-1 + #1) Pochhammer[1/2, -1 + #1])/Pochhammer[2, -1 + #1] &
Product[(4*i - 6)/i, {i, 2, x}] == g[x] // FullSimplify
True
Bobby
On Tue, 05 Jan 2010 00:48:02 -0600, Sam <sam.j.walke at gmail.com> 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?
>
--
DrMajorBob at yahoo.com
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