There is some Maxima code for finding explicit formulae for recursively
defined sequences.
Unfortunately, the code is so bug-ridden, I hesitate to encourage anyone
to try it. See
the bug report at
http://sourceforge.net/tracker/index.php?func=detail&aid=844521&group_id=4933&atid=104933
For your problem, Maxima is gets a correct value
(%i4) load("differ.mac")$
(%i6) difference(u[n]=2*u[n-1], u[n]);
difference: no u[n+1] term -- u[n] = 2*u[n-1]
(%o6) DONE
Okay, this doesn't seem to be the correct form for the input.....try
again.
(%i7) difference(u[n+1]=2*u[n], u[n]);
(%o7) u[n] = u[0]*2^n
Barton
Eric Delevaux <ericd@telefonica.net>
Sent by: maxima-admin@math.utexas.edu
09/07/2004 02:46 PM
To: maxima@math.utexas.edu
cc:
Subject: Re: [Maxima] define a sequence
Now i got my sequence u[n]=2*u[n-1]+1, no problem for the limit,
I tried
makelist(u[n],n,1,9);
to obtain u_1 to u_9. It does work. Is there another way? With map?
Is there a way to obtain the expression of u[n] in function of n with an
defintion by recurrance?
example :
u_0=3
u_n=2*u_{n-1}
<verynycemaxymafunctioninordertoobtain:>
u_n=3*2^n
Bye
Eric
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