I Need Help With This Equation

Eugene Shubert · Posted: Thu May 27, 2004 11:12 am Post subject: I Need Help With This Equation

Let A={real numbers x such that |x|<1}
Let S={real numbers Z such that 1 < Z < infinity}

Define ^ on A by the rule x^y = (x+y)/(1+xy).
It follows that (A, ^) is an Abelian group:

x^y=y^x
x^0=x
x^(-x)=0
x^(y^z)=(x^y)^z

I'm looking for a function from AxS->S (also written ^) such that, for any x, y, in A and any Z in S:

x^(y^Z) = (x^y)^Z

0^Z=Z
x^Z > Z if x>0
x^Z < Z if x<0

Thanks.