[VA] SRC #007 - 2020 April 1st Ramblings

[J-F Garnier]

(04-01-2020 06:52 PM)Valentin Albillo Wrote:  8)
...
Now consider the function exp(exp(z)), which is also an entire function, with a power series convergent everywhere and all that jazz. Being of the form exp(something) it omits 0 because exp(z) does. But then it also omits 1 ( = exp(0) )... contradicting Picard's LT. So I wonder: what gives ?

Of course, it doesn't omit 1 :
let's z=log(i*2*Pi*n) , n<>0
exp(exp(z)) = exp(i*2*Pi*n) = 1

Picard's Little Theorem is safe :-)

J-F