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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




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