Mathematica 9 is now available
Services & Resources / Wolfram Forums / MathGroup Archive
-----

MathGroup Archive 2010

[Date Index] [Thread Index] [Author Index]

Search the Archive

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


  • Prev by Date: Re: Re: Re: algebraic numbers
  • Next by Date: Re: NDSolve problem with switching
  • Previous by thread: RSolve problem: won't solve convolution recurrence relation.
  • Next by thread: Re: RSolve problem: won't solve convolution recurrence relation.