Re: Definition of an exponential function
- To: mathgroup at smc.vnet.net
- Subject: [mg31685] Re: [mg31665] Definition of an exponential function
- From: BobHanlon at aol.com
- Date: Sat, 24 Nov 2001 16:43:57 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
In a message dated 2001/11/23 6:45:02 AM, psino at tee.gr writes:
>I want to define a function with the properties of Exp.
>The definition
>f[x_+y_]:=f[x]f[y]
>f[m_ x_]:=f[x]^m
>f[0]=1
>gives
>f[x]^2 f[-x]^2=1
>but
>f[x]^m f[-x]^m=(1/f[x])^m (f[x])^m.
>Is there a way in Mathematica 4.1 to obtain f[x]^m f[-x]^m=1?
>
f[x_+y_]:=f[x]f[y];
f[m_ * x_]:=f[x]^m;
f[0]=1;
Table[f[x]^m * f[-x]^m, {m, -5, 5}]
{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}
Simplify[f[x]^m * f[-x]^m, Element[m, Integers]]
1
f[x]^m * f[-x]^m // PowerExpand
1
Bob Hanlon
Chantilly, VA USA