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Topic: Noob requests help with recursive formula
Replies: 2   Last Post: Mar 16, 2013 3:13 AM

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Ray Koopman

Posts: 3,382
Registered: 12/7/04
Re: Noob requests help with recursive formula
Posted: Mar 14, 2013 7:13 AM
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On Mar 13, 1:18 am, Garcia5...@yahoo.fr wrote:
> I have two lists, each with 99 elements; A and B. Real numbers.
> I want to form a list, C, whose elements are functions (F[])
> of A and B, and also previous elements of C itself.
>
> C = {F[A1/B1], F[A2/(B2-A1/C1)], F[A3/(B3-A1/C1-A2/C2)], ...,
> F[A99/(B99-A1/C1 ... -A98/C98.)}


...where the integers after A,B,C are element indices.

First define a helper function:

cr[{c_,r_},{a_,b_}] := {#, r+a/#}& @ f[a/(b-r)]

Then use FoldList. Here is an example with 3 elements:

Rest@FoldList[cr,{0,0},Transpose@
{{a1,a2,a3},{b1,b2,b3}}][[All,1]] //InputForm

{f[a1/b1],
f[a2/(b2 - a1/f[a1/b1])],
f[a3/(b3 - a1/f[a1/b1] - a2/f[a2/(b2 - a1/f[a1/b1])])]}





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