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

**References**:**RSolve problem: won't solve convolution recurrence relation.***From:*Sam <sam.j.walke@gmail.com>