# AuTra

AuTra or **ArcTra** or ArcTrappmann function is the inverse function of SuTra.

AuTra is Abel function of the Trappmann function, $\mathrm{tra}(z)=z+\exp(z)$.

AuTra satisfies the Abel equation

$ \mathrm{AuTra} \Big( \mathrm{tra}(z) \Big)= \mathrm{AuTra}(z)+1$

and the additional condition

$ \mathrm{AuTra}(1)=0$

This condition corresponds to relation $\mathrm{SuTra}(0)=1$. The same choice of the initial value is used also for many other superfunctions, including tetration, SuZex function, Tania function and Shoka function.

AuTra is real-holomorphic, $\mathrm{AuTra}(z^*)=\mathrm{AuTra}(z)^*$

## Branch points and the cut lines

AuTra has two branch points $~-1\!+\!\mathrm i~$ and $~-1\!-\!\mathrm i~$; the cut lines are directed to the left hand side of the complex plane, parallel to the real axis. In TORI, this is default choice of the cut lines.