09/15/2022, 11:59 PM
Let f(z) be an analytic function.
let z1 , z2 be complex numbers of the form a^2 + b^2 i and c^2 + d^2 i
such that Re ln(z1 + z2) =< ln (sqrt(2))
Let z_0 not be a fixpoint or cyclic point or singularity or pole of f(z).
and let f^[z1 + z2](z_0) = f^[w](z_0) = f^[z_1](f^[z_2](z_0)) = f^[z_2](f^[z_1](z_0))
For all z1,z2 such that z1 + z2 = w.
Let s = g^2 + h^2 i
Also let f^[s](z_0) be injective for all complex 0 =< s =< w.
then
f^[s](z_0) is analytic in s if 0 =< s =< w.
(the inequalities refer to the modulus comparisons)
Regards
tommy1729
let z1 , z2 be complex numbers of the form a^2 + b^2 i and c^2 + d^2 i
such that Re ln(z1 + z2) =< ln (sqrt(2))
Let z_0 not be a fixpoint or cyclic point or singularity or pole of f(z).
and let f^[z1 + z2](z_0) = f^[w](z_0) = f^[z_1](f^[z_2](z_0)) = f^[z_2](f^[z_1](z_0))
For all z1,z2 such that z1 + z2 = w.
Let s = g^2 + h^2 i
Also let f^[s](z_0) be injective for all complex 0 =< s =< w.
then
f^[s](z_0) is analytic in s if 0 =< s =< w.
(the inequalities refer to the modulus comparisons)
Regards
tommy1729