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