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Re: Replace in recursive equations
 To: mathgroup at smc.vnet.net
 Subject: [mg54392] Re: Replace in recursive equations
 From: David Bailey <dave at Remove_Thisdbailey.co.uk>
 Date: Sun, 20 Feb 2005 00:07:51 0500 (EST)
 References: <cv6s9k$6lr$1@smc.vnet.net>
 Sender: ownerwrimathgroup at wolfram.com
Skirmantas wrote:
> The last sentence of my previous message about Inverse got somehow
> scrambled. I meant "I have to reinput the output to get the result."
>
> One more quick question. Suppose I have a recursive equation F[n+1]==a
> F[n]. I want to replace F[n]>FF[n]+Q for _all_ n's. Q is a constant.
> What is the best way to do it? The left side should become FF[n+1]+Q
> and the right a(FF[n]+Q). Any help would be appreciated.
>
I think you really mean for all instances of the function F  I mean,
you would presumably want to replace F[3] if it appeared in the
equation. Thinking about it that way, the answer is easy:
eq = (F[n + 1] == a F[n])
eq /. F[z_] > FF[z] + Q
Q + FF[1 + n] == a*(Q + FF[n])
If you think you might need nested expressions  F[F[n]+1]  then you
will need to use //. . However, it is best to use this only if you need
to because if you make a mistake you can easily put Mathematica in a loop.
David Bailey
dbaileyconsultancy.co.uk
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