01/12/2015, 12:46 AM
I wonder if sexp(z) can be periodic.
In particular 2pi i periodic.
A search for period(ic) gives too many results.
SO forgive me if this has been asked/answered before.
If I recall correctly a pseudoperiod of 2 pi i / L is known to be possible ( L is a fixed point of exp ) because of f(z) = lim exp^[n](L^(z-n)) and similar limits.
Im unaware of limit formula's that give a periodic solution.
Maybe pentation helps us out , although I want to avoid adding this function.
Maybe the system of equations is overdetermined ??
f(0) = 1
f(z+a) = f(z)
f(z+1) = exp(f(z))
On the other hand maybe it has uniqueness ?
I think it has uniqueness if it has existance.
Reason is f(z+theta(z)) = f(z+a+theta(z+a)) Implies that
theta(z) is both '1' and 'a' periodic HENCE double periodic ;
A nonconstant theta can thus not be entire here !
COMBINE THAT WITH THE RIEMANN MAPPING THEOREM AND
nonconstant theta(z) cannot exist !!!
( I think )
regards
tommy1729
In particular 2pi i periodic.
A search for period(ic) gives too many results.
SO forgive me if this has been asked/answered before.
If I recall correctly a pseudoperiod of 2 pi i / L is known to be possible ( L is a fixed point of exp ) because of f(z) = lim exp^[n](L^(z-n)) and similar limits.
Im unaware of limit formula's that give a periodic solution.
Maybe pentation helps us out , although I want to avoid adding this function.
Maybe the system of equations is overdetermined ??
f(0) = 1
f(z+a) = f(z)
f(z+1) = exp(f(z))
On the other hand maybe it has uniqueness ?
I think it has uniqueness if it has existance.
Reason is f(z+theta(z)) = f(z+a+theta(z+a)) Implies that
theta(z) is both '1' and 'a' periodic HENCE double periodic ;
A nonconstant theta can thus not be entire here !
COMBINE THAT WITH THE RIEMANN MAPPING THEOREM AND
nonconstant theta(z) cannot exist !!!
( I think )
regards
tommy1729
