entire function close to sexp ??

[tommy1729]

Is there an entire function known that is close to sexp(z) near the positive real line ?

Such a function must exist.
Never read about it though.

Apart from interpolation I do not know in what way this should be constructed.

regards

tommy1729

Tommy,
There are many examples of entire superexponentials, such as iterating

f(z)=b^z, where b=exp(1/e), jaydfox calls this "cheta(z)", fixpoint=e
f(z)=exp(z)-1, this turns out to be cheta(z)/e-1, fixpoint=0
f(z)=2sinh(z), fixpoint=0
f(z)=sinh(z), fixpoint=0
f(z)=b^z, from the upper fixed point for bases less than 1<b<exp(1/e)

All of them grow super-exponentially at the real axis, and they are entire, but they don't behave like sexp(z) near z=0.
- Sheldon

Right. Sorry I should have remembered.