elementary superfunctions

[tommy1729]

I've verified both and both indeed correct solutions. Mathematica finds \( F(x)=C^{b^x} \) for the general case of \( f(x)=x^b \).

What Maple gives for \( f(x)=\frac{x+a}{x-a} \)?

Nothing

hasnt this been solved before ?

regarding my critisism ( in a previous post in this thread ) that only ( elementary or other ) superfunctions of polynomials , a x ^ b or moebius functions are known ;

a challange :

what is the superfunction of

(a x ^ 2 + b x + c) / ( A x^2 + B x + C )

( yes, it can in some cases be reduced , common factors divided away , different cases occur ( different amount and position of fixpoints ) , i know that ... )


i sometimes call this superfunction " generalized sine / cosine "

( on sci.math e.g. )

regards

tommy1729