       Re: Recursive function

• To: mathgroup at smc.vnet.net
• Subject: [mg115915] Re: Recursive function
• From: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>
• Date: Tue, 25 Jan 2011 06:31:26 -0500 (EST)
• References: <ihm4kn\$kec\$1@smc.vnet.net>

```You need to make x explicitely depend on a and b as well:

ClearAll[x];
x[t_, a_, b_] := a*x[t - 1, a, b] + b*x[t - 2, a, b]
x[0, a_, b_] = 1;
x[1, a_, b_] = 1;
Manipulate[
Map[x[#, a, b] &, Range[0, 3]], {a, -1, 1, 0.5}, {b, -1, 1, .5}]

Cheers -- Sjoerd

On Jan 25, 10:20 am, StatsMath <stats.ma... at gmail.com> wrote:
> I am trying to compute the following function:
>
> x[t] = a * x[t-1] + b * x[t-2]
> x = 1
> x = 1
>
> For different values of a & b.
>
> Would like to use Manipulate[] so that I can change the values of a &
> b dynamically and observe what the resulting x[t] values are.
>
> So wrote the following piece of code:
>
> Clear["Global`*"]
> x[t_Integer] := x[t] = a x[t - 1] + b x[t - 2]
> x = 1;
> x = 1;
> Manipulate[Map[x[#] &, Range[0, 3]], {a, -1, 1, 0.5}, {b, -1, 1, .5}]
>
> Got the following results:
> {1, 1, a + b, b + a (a + b)}
>
> The a & b values are not being propagated so tried the following:
>
> Clear["Global`*"]
> x[t_Integer] := x[t] = a x[t - 1] + b x[t - 2] /; t > 2
> x = 1;
> x = 1;
> Manipulate[
>  Map[(If[# == 0 || # == 1, 1, a x[# - 1] + b x[# - 2]]) &,
>   Range[0, 3]], {a, -1, 1, 0.5}, {b, -1, 1, .5}]
>
> Got the following result:
> {1, 1, -2, -1 - a - b}
>
> Finally got it working with the following code:
>
> Clear["Global`*"]
> Manipulate[
>  Map[(If[# == 0 || # == 1, x[#] = 1,
>      x[#] = a x[# - 1] + b x[# - 2]]) &, Range[0, 20]], {a, -1, 1=
,
>   0.5}, {b, -1, 1, .5}]
>
> The above code looks ugly, so wondering if there is a different way to
> handle recursive functions.
>
> Thanks!

```

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