I wanted to ask another question. Got curious outside the basics, perhaps.

What if we contruct a 2 variable function F(t,x) where t is iteration of f(x) , x - argument of f(x) and then parametrize, for example:

t=g(y); x= h(y) , so

F(g(y), h(y) ) ;

Now, we can assume various functions g, h with different growth speeds. For example, we may consider:

g(y) = y!, h(y) = e^y or,

g(y) =e^y, h(y) = y! or any other.

It could be also possible to make t an imaginary part of a complex number, while x would be real part, so that:

So then F(t,x) becomes F(z) if functions h(y) and g(y) satisfy Euler conditions for derivatives of complex number functions.

What I wanted to ask, is , has this been considered, where could I read about it and does it make any sense at all to look at such functions?

Ivars

What if we contruct a 2 variable function F(t,x) where t is iteration of f(x) , x - argument of f(x) and then parametrize, for example:

t=g(y); x= h(y) , so

F(g(y), h(y) ) ;

Now, we can assume various functions g, h with different growth speeds. For example, we may consider:

g(y) = y!, h(y) = e^y or,

g(y) =e^y, h(y) = y! or any other.

It could be also possible to make t an imaginary part of a complex number, while x would be real part, so that:

So then F(t,x) becomes F(z) if functions h(y) and g(y) satisfy Euler conditions for derivatives of complex number functions.

What I wanted to ask, is , has this been considered, where could I read about it and does it make any sense at all to look at such functions?

Ivars