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