Again I didn't see some simplification...

Here it is:

this is

second power of g(z) (not "iterate"!)

where c(a,b) is binomial(a,b) and this gives a binomial-matrix column-shifted accordingly to powers of g.

Can we describe the half-iterate from this?

Here it is:

Code:

`´ using g(z)= e z^2 + (1+(p-q)) z`

setting e = (1+(p-q))

Code:

`´ g(z)= e z (z + 1)`

second power of g(z) (not "iterate"!)

Code:

`´ (g(z))^2 = e^2 z^2 (z+1)^2 = e^2 z^2 (c(2,0)z^2 + c(2,1)z + c(2,2) )`

where c(a,b) is binomial(a,b) and this gives a binomial-matrix column-shifted accordingly to powers of g.

Can we describe the half-iterate from this?

Gottfried Helms, Kassel