Revision as of 06:58, 1 December 2018 by Maintenance script (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search
$f=\mathrm{ArcTania}(x\!+\!{\rm i} y)$ in the $x,y$ plane with levels $u\!=\!\Re(f)\!=\! \mathrm {const} ~$ and $v\!=\!\Im(f)\!=\! \mathrm {const} ~$

ArcTania is [[elementary function,


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)} $


  1. D.Kouznetsov. Superfunctions for amplifiers. Optical Review, July 2013, Volume 20, Issue 4, pp 321-326.


Doya function, Inverse function, Tania