ArcTania

ArcTania is [[elementary function,

\(\mathrm{ArcTania}(z)=z+\ln(z)−1\)

Complex map of ArcTania is shown in figure at right.

ArcTania is important, because its inverse function \(\mathrm{Tania}=\mathrm{ArcTania}^{-1}\), is est, the Tania function, appears in the Laser science as solution of the equation of evolution of intensity of light in the idealised saturable amplifier :

\( \displaystyle \mathrm{Tania}^{\prime}(z)=\frac{\mathrm{Tania}(z)}{1+\mathrm{Tania}(z)} \)

Keywords
Doya function, Inverse function, Tania