using sinh(x) ?

[sheldonison]

thanks for the reply.

that is intresting.

however i dont think it is the same ,

i do it differently , although the end result may be the same ;

for real x and y , both >=0 :

let g(x,y) be the y'th iterate of exp(x) evaluated at x.

let f(x,y) be the y'th iterate of 2 sinh(x) evaluated at x.

How do you calculate f(x,y)? I would drop the "x" term entirely... I calculate f(y) using the superfunction equation I gave. If f(z)=2^z is a small number, then it approximates the behavior of the superfunction for 2sinh. Do you have a different equation, and could you share it?



After that, do you agree that converting from your f(y) to g(y) by iterating natural logarithms would appear to be exactly the same? Here, the superfunction <=> f(y), and TommySexp <=> g(y). The only reason I threw in the "k" constant was so that the resulting sexp_e(z) can be normalized so that TommySexp_e(0)=1. Otherwise, with the k constant=0, I get TommySexp(0)=0.92715... The value I'm using for k is 0.067838366.

then g(x,y) = lim k -> oo
log log log ... (k times ) [f( g(x,k) ,y)]


regards

tommy1729

btw g(x,y) satisfies ( derivative with respect to x )
g'(x,y) / g'(exp(x),y) = exp(x)/F(exp(x)

but i guess you already knew that.

Nope, certainly didn't, nor do I understand it But if it holds in the complex plane, that would really be something, since g and f are such different functions. f is the super function of 2sinh, and g is the iterated natural logarithm (n times) of f(z+n). Do you think g(x) is analytic (as n=>oo)?