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? >