Difference between revisions of "ArcTania"
m (Text replacement  "\$([^\$]+)\$" to "\\(\1\\)") 

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−  [[File:ArcTaniaMap.pngright350pxthumb 
+  [[File:ArcTaniaMap.pngright350pxthumb \(f=\mathrm{ArcTania}(x\!+\!{\rm i} y)\) in the \(x,y\) plane with levels 
−  +  \(u\!=\!\Re(f)\!=\! \mathrm {const} ~\) and 

−  +  \(v\!=\!\Im(f)\!=\! \mathrm {const} ~\)]] 

[[ArcTania]] is [[elementary function, 
[[ArcTania]] is [[elementary function, 

−  +  \(\mathrm{ArcTania}(z)=z+\ln(z)−1\) 

[[Complex map]] of [[ArcTania]] is shown in figure at right. 
[[Complex map]] of [[ArcTania]] is shown in figure at right. 

−  [[ArcTania]] is important, because its inverse function 
+  [[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 
appears in the [[Laser science]] as solution of the equation of evolution of intensity of light in the idealised saturable amplifier 

<ref> 
<ref> 

Line 17:  Line 17:  
</ref>: 
</ref>: 

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

==References== 
==References== 
Latest revision as of 18:43, 30 July 2019
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/s1004301300586
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 321326.