07/02/2011, 10:32 PM
\( \operatorname{TommySexp_e}(z,x)= \lim_{n \to \infty } \ln^{[n]} (\operatorname{2sinh}^{[z]}(\exp^{[n]}(x))) \)
i can now prove a positive radius in x when expanded at certain points and Coo for real z.
i assume that can be strengthened to analytic in both x and z with some effort (and perhaps a good book). ( see lemma 1 * add link later * )
however i wont go into details here yet , im currently more intrested in other things about tetration and perhaps this should make a good paper.
in particular i still dont know why 1.729 i ^1.729 i ^ ... 0.5 + 0.5 i gives a circle and that bothers me.
i can now prove a positive radius in x when expanded at certain points and Coo for real z.
i assume that can be strengthened to analytic in both x and z with some effort (and perhaps a good book). ( see lemma 1 * add link later * )
however i wont go into details here yet , im currently more intrested in other things about tetration and perhaps this should make a good paper.
in particular i still dont know why 1.729 i ^1.729 i ^ ... 0.5 + 0.5 i gives a circle and that bothers me.