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Re: Recursion relation

• To: mathgroup at yoda.physics.unc.edu
• Subject: Re: Recursion relation
• From: a_rubin at dsg4.dse.beckman.com (arthur rubin)
• Date: Fri, 10 Jul 92 07:43:25 PDT

You (martind at puhep1.princeton.edu) write:
   I'm trying to implement the following recursion relation for a
certain index function c[i]:



   c[i] = r[i]  - a[i,i-1]*c[i-1]


where r[i] and a[i,i-1] are given functions.

  Namely, I'd like to have a function c[i+n_Integer] giving me the
expression of  

   c[i+n]

in terms of 


   r[i+n],r[i+n-1],...,r[i] and c[i-1].

  DOES ANYBODY KNOW A WAY TO DO THIS ???
------------------------------------------------------------------------------

c[X:i_Symbol + Optional[n_Integer]] := r[X] - a[X,X-1] c[X-1] /; n >= 0

or 
c[X] = cc[X+1]
cc[X:_ + _Integer?Positive] := r[X-1] - a[X-1,X-2] cc[X-1]
Format[cc[X_]] := HoldForm[c][X-1]