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

```

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