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MathGroup Archive 1998

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Re: recursive relation problem ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg13678] Re: [mg13656] recursive relation problem ?
  • From: BobHanlon at aol.com
  • Date: Sat, 15 Aug 1998 04:39:10 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Needs["DiscreteMath`RSolve`"]

RSolve[{f[0] == f[1] == 1, f[n] == n*f[n - 1]}, f[n], n]

{{f[n] -> n!}}

However, the second initial condition is unnecessary:

RSolve[{f[0] == 1, f[n] == n*f[n - 1]}, f[n], n]

{{f[n] -> n!}}

Another example:

Simplify[RSolve[{f[0] == 0, f[1] == 1, 
    f[n] == f[n - 1] + f[n - 2]}, f[n], n]]

{{f[n] -> -(((1/2*(1 - Sqrt[5]))^n - (1/2*(1 + Sqrt[5]))^n)/
       Sqrt[5])}}

Bob Hanlon

In a message dated 8/11/98 6:28:53 AM, cplai at geocities.com wrote:

>I am studying data structure, and always encounter recursive relation
>equations. How do I use mathematica to give general solution of
>recursive relation.
>
>For example: f(0)=1; f(1)=1; f(x)=x*f(x-1);


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