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*: owner-wri-mathgroup at wolfram.com

Skirmantas wrote: > The last sentence of my previous message about Inverse got somehow > scrambled. I meant "I have to re-input 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