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