as a sidenote to the above :
notice that if a function has no identity , this often results in the equivalent of a value that cannot be attained.
if f(z) is entire and has values that cannot be attained ;
it is of type exp(entire(z)) + Constant.
hence we tend to have solutions of type exp^[a](exp^[b](x) + exp^[b](y)).
but more can be said.
you might wanna read this old but good thread containing an intresting proof by bo :
http://math.eretrandre.org/tetrationforu...hp?tid=125
regards
tommy1729
notice that if a function has no identity , this often results in the equivalent of a value that cannot be attained.
if f(z) is entire and has values that cannot be attained ;
it is of type exp(entire(z)) + Constant.
hence we tend to have solutions of type exp^[a](exp^[b](x) + exp^[b](y)).
but more can be said.
you might wanna read this old but good thread containing an intresting proof by bo :
http://math.eretrandre.org/tetrationforu...hp?tid=125
regards
tommy1729