03/21/2014, 10:31 PM

https://sites.google.com/site/tommy1729/...e-property

We use a uniqueness condition on sexp : for x,y >=0 : sexp(x+yi) is real entire.

We could change the base e to base 2 or change tetration to pentation to generalize things.

Imho that is the way to do hyperoperation and I believe that answers almost all questions. ( I read your paper ).

Imho there are 2 big questions remaining :

1) informally speaking : what lies between tetration and pentation ?

Once again I mean the " half-super functions " as has been discussed on this forum before ( mainly by myself and James Nixon ).

Let S mean "superfunction of ..." and S^[-1] "is the superfunction of ..."

We have S^[-1](f(x)) = f ( f^[-1](x)+1)

examples :

S(exp(x)) = sexp(x)

S^[-1](sexp(x)) = sexp(slog(x)+1) = exp(x)

Question : if we say S^[a+b](f(x)) = S^[a](S^[b](f(x)) = S^[b](S^[a](f(x))

Then what is S^[1/2](f(x)) ? Or what is S^[1/2](exp(x)) ?

(Question 2 is still under investigation and not formulated yet)

regards

tommy1729

We use a uniqueness condition on sexp : for x,y >=0 : sexp(x+yi) is real entire.

We could change the base e to base 2 or change tetration to pentation to generalize things.

Imho that is the way to do hyperoperation and I believe that answers almost all questions. ( I read your paper ).

Imho there are 2 big questions remaining :

1) informally speaking : what lies between tetration and pentation ?

Once again I mean the " half-super functions " as has been discussed on this forum before ( mainly by myself and James Nixon ).

Let S mean "superfunction of ..." and S^[-1] "is the superfunction of ..."

We have S^[-1](f(x)) = f ( f^[-1](x)+1)

examples :

S(exp(x)) = sexp(x)

S^[-1](sexp(x)) = sexp(slog(x)+1) = exp(x)

Question : if we say S^[a+b](f(x)) = S^[a](S^[b](f(x)) = S^[b](S^[a](f(x))

Then what is S^[1/2](f(x)) ? Or what is S^[1/2](exp(x)) ?

(Question 2 is still under investigation and not formulated yet)

regards

tommy1729