# 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
^{[1]}:

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

## References

- ↑
http://link.springer.com/article/10.1007/s10043-013-0058-6

http://mizugadro.mydns.jp/PAPERS/2013or1.pdf

http://mizugadro.mydns.jp/PAPERS/2013or2.pdf D.Kouznetsov. Superfunctions for amplifiers. Optical Review, July 2013, Volume 20, Issue 4, pp 321-326.