elementary superfunctions

[tommy1729]

Summary: \( F(x)=\exp(a^x)c^{\frac{1}{1-a}} \) is an elementary superfunction of \( f(x)=cx^a \), for \( a\neq 1 \).

this result is far from new.

---

'in general' super-functions are of hypergeometric or inverse hypergeometric " kind " , where " kind " mainly denotes nested structures.

and with ' in general ' i mean usually if the (original) function is elementary.

i advocated the concept of inverse hypergeometric functions before , as e.g. on sci.math but without much results.

usually , if we arrive at an integral expression for our super-function its hypergeometric or inverse hypergeometric.

and that can often be reduced to elementary by using 'integral calculus'.


i tried to related all of this to half iterations of exp(x) but nothing worked.

mainly because exp(x) lacks a real fixpoint and a real zero at the same time ....


regards

tommy1729