Re: iterations, recursions and derivatives
- To: mathgroup at smc.vnet.net
- Subject: [mg22561] Re: [mg22544] iterations, recursions and derivatives
- From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
- Date: Sat, 11 Mar 2000 17:52:37 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
on 3/9/00 9:24 AM, Otto Linsuain at linsuain+ at andrew.cmu.edu wrote:
>
> Hello. I find it hard to define a sequence of functions recursively and
> be able to differenciate them at the same time. For example
>
> f[x_,1]:=x^2
>
> Try to differentiate Derivative[1,0][f][2,1] will not work. Changing :=
> for = doesn't help. Can do:
>
> f[x_,1_]:=x^2 Notice the _ after the 1 (Kind of wierd, isn't it?)
>
> Now, however, can differentiate: Derivative[1,0][f][2,1] works fine.
> But cannot work recursions:
>
> f[x_,m_]:= SomeOperation[f[x,m-1]] confuses the recursion process. I
> have tried defining
>
> f[x_,m_]:=If[m==1,x^2,SomeOperation[f[x,m-1]], but the recursion again
> crashes.
>
> I have tried Which, Switch, Condition, Dt, D, etc, but to no avail.
> When I can take the derivative, I can't update m to m+1.
>
> Any suggestions? Thanks, Otto Linsuain.
>
>
You do not explain clearly enough what you want to do. For example, is the
following satisfactory?
In[1]:=
f[1][x_] := x^2
In[2]:=
f[n_][x_] := Sin[f[n - 1][x^n]]
In[3]:=
Derivative[1][f[5]][x]
Out[3]=
239 240 240 240
240 x Cos[x ] Cos[Sin[x ]] Cos[Sin[Sin[x ]]]
240
Cos[Sin[Sin[Sin[x ]]]]
--
Andrzej Kozlowski
Toyama International University
JAPAN
http://sigma.tuins.ac.jp