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iterations, recursions and derivatives

• To: mathgroup at smc.vnet.net
• Subject: [mg22544] iterations, recursions and derivatives
• From: Otto Linsuain <linsuain+ at andrew.cmu.edu>
• Date: Thu, 9 Mar 2000 03:24:29 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

 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. 

• Follow-Ups:
  • Re: iterations, recursions and derivatives
    • From: Hartmut Wolf <hwolf@debis.com>
  • Re: iterations, recursions and derivatives
    • From: Otto Linsuain <linsuain+@andrew.cmu.edu>