- #1
Perfectly Innocent
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This post is a sincere request for help. I assume that the following problem can be represented by a differential equation and that only a mathematician can solve it.
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
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