[entire exp^0.5] The half logaritm. - Printable Version +- Tetration Forum ( https://math.eretrandre.org/tetrationforum)+-- Forum: Tetration and Related Topics ( https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=1)+--- Forum: Mathematical and General Discussion ( https://math.eretrandre.org/tetrationforum/forumdisplay.php?fid=3)+--- Thread: [entire exp^0.5] The half logaritm. ( /showthread.php?tid=864) |

[entire exp^0.5] The half logaritm. - tommy1729 - 05/11/2014
If f is entire and grows not faster than exp(|z|) on the complex plane, it either takes all values or it is exp(az+b)+c. Therefore since f takes all values, ln(f) has at least 1 logaritmic singularity. Now let f be our beloved entire approximation of exp^[1/2]. Then it follows exp^[1/2] and exp^[-1/2] cannot both be entire. In fact exp^[-1/2] is never entire because it is independant of the entirehood of exp^[1/2]. ( a logarithm of a nonentire function is also nonentire ! ) Ofcourse this does not yet rule out an entire exp^[-1/2] if we allow a "fake" log. However Im worried about how good of an approximation a fake log would give us. The story is getting " complex ". regards tommy1729 RE: [entire exp^0.5] The half logaritm. - tommy1729 - 05/11/2014
The weierstrass product expansion also seems mysterious ? regards tommy1729 |