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Re: nested derivatives

  • To: mathgroup at smc.vnet.net
  • Subject: [mg93117] Re: nested derivatives
  • From: Peter Pein <petsie at dordos.net>
  • Date: Mon, 27 Oct 2008 03:12:28 -0500 (EST)
  • References: <ge14fc$9g2$1@smc.vnet.net>

Huub Mooren schrieb:
> How do I enter the following recursive function in Mathematica:
> t[n]=(1/y')*t'[n-1],
> with n the index
> t[0]=x
> y is some function of x
> 
> Thanks for your help.
> 
> Huub Mooren
> 
I would try:
Subscript[t, 0][x_] = x;
Subscript[t, n_][x_] := Derivative[1][Subscript[t, n - 1]][x] /
Derivative[1][y][x]

Block[{y = Exp}, Table[Subscript[t, n][x], {n, 0, 5}]]
yields
{x, E^(-x), -E^(-2*x), 2/E^(3*x), -6/E^(4*x), 24/E^(5*x)}

Peter



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