Congratulations! This opens whole lot of new worlds.
Not afraid, but difficult for me to work with before I learn enough software how to handle complex number iterations... I love them, at least imaginary unit
So You mean Your formula works at least in the range \( e^{-e}; e^{1/e} \) also below 1? That is wonderful achievement because it leads to infinity of very simple exactly definable points of negative real heights (when a<1, \( a^{1/a}[4]{1/\ln(a)}=1 \) which can also be utilized to check various real and complex heigths calculation approaches.
For base \( {1/e} \), \( {1/e}[4]-{1/\Omega} =1 \) - you can add this to your graph as well perhaps another spiral will emerge which should pass via this point?
Your nice spiral graph (see-spirals are involved) anyway converges to my beloved \( \Omega \), as it should as \( {1/e}[4]\infty=\Omega=0.567143.. \).
Which just confirms its true. But what about base \( e^{1/e} \) which is limit case?
Ivars
bo198214 Wrote:As it seems that Ivars is too fearful of complex numbers.
Not afraid, but difficult for me to work with before I learn enough software how to handle complex number iterations... I love them, at least imaginary unit
So You mean Your formula works at least in the range \( e^{-e}; e^{1/e} \) also below 1? That is wonderful achievement because it leads to infinity of very simple exactly definable points of negative real heights (when a<1, \( a^{1/a}[4]{1/\ln(a)}=1 \) which can also be utilized to check various real and complex heigths calculation approaches.
For base \( {1/e} \), \( {1/e}[4]-{1/\Omega} =1 \) - you can add this to your graph as well perhaps another spiral will emerge which should pass via this point?
Your nice spiral graph (see-spirals are involved
) anyway converges to my beloved \( \Omega \), as it should as \( {1/e}[4]\infty=\Omega=0.567143.. \).Which just confirms its true. But what about base \( e^{1/e} \) which is limit case?
Ivars
