       Re: Noob requests help with recursive formula

• To: mathgroup at smc.vnet.net
• Subject: [mg130150] Re: Noob requests help with recursive formula
• From: Ray Koopman <koopman at sfu.ca>
• Date: Thu, 14 Mar 2013 07:15:30 -0400 (EDT)
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• Delivered-to: l-mathgroup@wolfram.com
• Delivered-to: mathgroup-newout@smc.vnet.net
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• References: <khpco1\$mdi\$1@smc.vnet.net>

```On Mar 13, 1:18 am, Garcia5... at 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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