Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











ArcTanh




Mathematica Notation

Traditional Notation









Elementary Functions > ArcTanh[z] > Representations through equivalent functions > With related functions





Involving sinh-1

Involving tanh-1(z)

Involving tanh-1(z) and sinh-1(2 z/1-z2)

>
>
>
>
>

Involving tanh-1(z)and sinh-1(2 z/z2-1)

>
>
>
>
>

Involving tanh-1(z) and sinh-1(i(1+z2)/1-z2)

>
>
>
>
>

Involving tanh-1(z) and sinh-1(i (z2+1)/z2-1)

>
>
>
>
>

Involving tanh-1(z) and sinh-1(1/(z2-1)1/2)

>
>
>
>
>

Involving tanh-1(z) and sinh-1(1/z2-11/2)

>
>
>
>
>

Involving tanh-1(z) and sinh-1(z/(1-z2)1/2)

>
>
>
>

Involving tanh-1(z) and sinh-1((z2)1/2/(1-z2)1/2)

>
>
>
>
>

Involving tanh-1(z) and sinh-1((-z2)1/2/(z2-1)1/2)

>
>
>
>
>

Involving tanh-1(z) and sinh-1(z2/1-z21/2)

>
>
>
>
>

Involving tanh-1(z) and sinh-1((-(1-z2)1/2-1)1/2/(21/2(1-z2)1/4))

>
>
>
>
>

Involving tanh-1(z) and sinh-1((1-(1-z2)1/2)1/2/(21/2(1-z2)1/4))

>
>
>

Involving tanh-1(z) and sinh-1((-((1-z2)1/2+1)/(2(1-z2)1/2))1/2)

>
>
>
>
>

Involving tanh-1(z) and sinh-1(((1-(1-z2)1/2)/(2(1-z2)1/2))1/2)

>
>
>

Involving tanh-1(z) and sinh-1((-(z2-1)1/2-z)1/2/(21/2(z2-1)1/4))

>
>
>
>

Involving tanh-1(z) and sinh-1((z-(z2-1)1/2)1/2/(21/2(z2-1)1/4))

>
>
>
>

Involving tanh-1(z) and sinh-1((-((z2-1)1/2+z)/(2(z2-1)1/2))1/2)

>
>
>
>
>
>

Involving tanh-1(z) and sinh-1(((z-(z2-1)1/2)/(2(z2-1)1/2))1/2)

>
>
>
>
>
>

Involving tanh-1(z1/2)

Involving tanh-1(z1/2) and sinh-1(i(1+z)/1-z)

>
>
>
>

Involving tanh-1(z1/2) and sinh-1(i(z+1)/z-1)

>
>
>
>

Involving tanh-1(z1/2) and sinh-1(2 z1/2/1-z)

>
>
>
>
>

Involving tanh-1(z1/2) and sinh-1(2 z1/2/z-1)

>
>
>
>
>

Involving tanh-1(z1/2) and sinh-1(1/(z-1)1/2)

>
>
>
>

Involving tanh-1(z1/2) and sinh-1(1/z-11/2)

>
>
>
>

Involving tanh-1(z1/2) and sinh-1(z1/2/(1-z)1/2)

>
>
>

Involving tanh-1(z1/2) and sinh-1((-z)1/2/(z-1)1/2)

>
>
>
>

Involving tanh-1(z1/2) and sinh-1(z/1-z1/2)

>
>
>

Involving tanh-1(z1/2) and sinh-1((-(1-z)1/2-1)1/2/(21/2(1-z)1/4))

>
>
>
>

Involving tanh-1(z1/2) and sinh-1((1-(1-z)1/2)1/2/(21/2(1-z)1/4))

>

Involving tanh-1(z1/2) and sinh-1((-((1-z)1/2+1)/(2(1-z)1/2))1/2)

>
>
>
>

Involving tanh-1(z1/2) and sinh-1(((1-(1-z)1/2)/(2(1-z)1/2))1/2)

>

Involving tanh-1(z1/2) and sinh-1((-(1-z)1/2-(-z)1/2)1/2/(21/2(1-z)1/4))

>
>
>
>

Involving tanh-1(z1/2) and sinh-1(((-z)1/2-(1-z)1/2)1/2/(21/2(1-z)1/4))

>
>
>
>

Involving tanh-1(z1/2) and sinh-1((-((1-z)1/2+(-z)1/2)/(2(1-z)1/2))1/2)

>
>
>
>

Involving tanh-1(z1/2) and sinh-1((((-z)1/2-(1-z)1/2)/(2(1-z)1/2))1/2)

>
>
>
>

Involving tanh-1(1/z1/2)

Involving tanh-1(1/z1/2) and sinh-1(i (1+z)/1-z)

>
>
>
>

Involving tanh-1(1/z1/2) and sinh-1(i(z+1)/z-1)

>
>
>
>

Involving tanh-1(1/z1/2) and sinh-1(2 z1/2/1-z)

>
>
>
>
>

Involving tanh-1(1/z1/2) and sinh-1(2 z1/2/z-1)

>
>
>
>
>

Involving tanh-1(1/z1/2) and sinh-1(1/(z-1)1/2)

>
>
>

Involving tanh-1(1/z1/2) and sinh-1(1/z-11/2)

>
>
>
>

Involving tanh-1(1/z1/2) and sinh-1(z1/2/(1-z)1/2)

>
>
>
>

Involving tanh-1(1/z1/2) and sinh-1((-z)1/2/(z-1)1/2)

>
>
>
>

Involving tanh-1(1/z1/2) and sinh-1(z/1-z1/2)

>
>
>

Involving tanh-1(1/z1/2) and sinh-1((-(1-z)1/2-1)1/2/(21/2(1-z)1/4))

>
>
>
>

Involving tanh-1(1/z1/2) and sinh-1((1-(1-z)1/2)1/2/(21/2(1-z)1/4))

>
>
>

Involving tanh-1(1/z1/2) and sinh-1((-((1-z)1/2+1)/(2(1-z)1/2))1/2)

>
>
>
>
>

Involving tanh-1(1/z1/2) and sinh-1(((1-(1-z)1/2)/(2(1-z)1/2))1/2)

>
>
>

Involving tanh-1(1/z1/2) and sinh-1((-(1-z)1/2-(-z)1/2)1/2/(21/2(1-z)1/4))

>
>
>
>
>

Involving tanh-1(1/z1/2) and sinh-1(((-z)1/2-(1-z)1/2)1/2/(21/2(1-z)1/4))

>
>
>
>

Involving tanh-1(1/z1/2) and sinh-1((-((1-z)1/2+(-z)1/2)/(2(1-z)1/2))1/2)

>
>
>
>

Involving tanh-1(1/z1/2) and sinh-1((((-z)1/2-(1-z)1/2)/(2(1-z)1/2))1/2)

>
>
>
>

Involving tanh-1((1+z)1/2)

Involving tanh-1((1+z)1/2) and sinh-1(1/z1/2)

>
>
>
>

Involving tanh-1((1+z)1/2) and sinh-1(1/z1/2)

>
>
>
>

Involving tanh-1(1/(1+z)1/2)

Involving tanh-1(1/(1+z)1/2) and sinh-1(1/z1/2)

>
>
>

Involving tanh-1(1/(1+z)1/2) and sinh-1(1/z1/2)

>
>
>
>

Involving tanh-1(1/1+z1/2)

Involving tanh-1(1/1+z1/2) and sinh-1(1/z1/2)

>
>
>

Involving tanh-1(1/1+z1/2) and sinh-1(1/z1/2)

>
>
>

Involving tanh-1((z+1)1/2/z1/2)

Involving tanh-1((z+1)1/2/z1/2) and sinh-1(z1/2)

>
>
>

Involving tanh-1((-1-z)1/2/(-z)1/2)

Involving tanh-1((-1-z)1/2/(-z)1/2) and sinh-1(z1/2)

>
>
>
>

Involving tanh-1(z+1/z1/2)

Involving tanh-1(z+1/z1/2) and sinh-1(z1/2)

>
>
>
>

Involving tanh-1(z1/2/(1+z)1/2)

Involving tanh-1(z1/2/(1+z)1/2) and sinh-1(z1/2)

>
>
>

Involving tanh-1((-z)1/2/(-1-z)1/2)

Involving tanh-1((-z)1/2/(-1-z)1/2) and sinh-1(z1/2)

>
>
>
>

Involving tanh-1(z/z+11/2)

Involving tanh-1(z/z+11/2) and sinh-1(z1/2)

>
>
>

Involving tanh-1((z-a)1/2/(z+a)1/2)

Involving tanh-1((z+1)1/2/(z-1)1/2) and sinh-1(i z)

>
>
>
>

Involving tanh-1((z-1)1/2/(z+1)1/2) and sinh-1(i z)

>
>
>
>

Involving tanh-1((a-z)1/2/(-a-z)1/2)

Involving tanh-1((-1-z)1/2/(1-z)1/2) and sinh-1(i z)

>
>
>
>

Involving tanh-1((1-z)1/2/(-1-z)1/2) and sinh-1(i z)

>
>
>
>
>

Involving tanh-1(z-a/z+a1/2)

Involving tanh-1(z+1/z-11/2) and sinh-1(i z)

>
>
>
>

Involving tanh-1(z-1/z+11/2) and sinh-1(i z)

>
>
>
>

Involving tanh-1((1+z2)1/2)

Involving tanh-1((1+z2)1/2) and sinh-1(1/z)

>
>
>
>
>

Involving tanh-1(1/(1+z2)1/2)

Involving tanh-1(1/(1+z2)1/2) and sinh-1(1/z)

>
>
>
>
>

Involving tanh-1(1/1+z21/2)

Involving tanh-1(1/1+z21/2) and sinh-1(1/z)

>
>
>
>
>

Involving tanh-1(z1+z2/z21/2)

Involving tanh-1(z1+z2/z21/2) and sinh-1(1/z)

>
>
>

Involving tanh-1(z/(z2+1)1/2)

Involving tanh-1(z/(z2+1)1/2) and sinh-1(z)

>
>
>
>

Involving tanh-1((z2)1/2/(1+z2)1/2)

Involving tanh-1((z2)1/2/(1+z2)1/2) and sinh-1(z)

>
>
>
>
>

Involving tanh-1((-z2)1/2/(-z2-1)1/2)

Involving tanh-1((-z2)1/2/(-z2-1)1/2) and sinh-1(z)

>
>
>
>
>

Involving tanh-1(z2/z2+11/2)

Involving tanh-1(z2/z2+11/2) and sinh-1(z)

>
>
>
>
>

Involving tanh-1((z2+1)1/2/z)

Involving tanh-1((z2+1)1/2/z) and sinh-1(z)

>
>
>

Involving tanh-1((z2+1)1/2/(z2)1/2)

Involving tanh-1((z2+1)1/2/(z2)1/2) and sinh-1(z)

>
>
>
>
>

Involving tanh-1((-1-z2)1/2/(-z2)1/2)

Involving tanh-1((-1-z2)1/2/(-z2)1/2) and sinh-1(z)

>
>
>
>
>

Involving tanh-1(z2+1/z21/2)

Involving tanh-1(z2+1/z21/2) and sinh-1(z)

>
>
>
>
>

Involving tanh-1((1+z2)1/2+a/z)

Involving tanh-1((1+z2)1/2+1/z) and sinh-1(z)

>
>
>

Involving tanh-1((1+z2)1/2-1/z) and sinh-1(z)

>

Involving tanh-1(z/(1+z2)1/2+a)

Involving tanh-1(z/(1+z2)1/2+1) and sinh-1(z)

>

Involving tanh-1(z/(1+z2)1/2-1) and sinh-1(z)

>
>
>

Involving tanh-1(2 (1+z2)1/2/2+z2)

Involving tanh-1(2 (1+z2)1/2/2+z2) and sinh-1(1/z)

>
>
>
>

Involving tanh-1(2+z2/2 (1+z2)1/2)

Involving tanh-1(2+z2/2 (1+z2)1/2) and sinh-1(1/z)

>
>
>
>
>
>
>

Involving tanh-1(2 z (z2+1)1/2/1+2z2)

Involving tanh-1(2 z (z2+1)1/2/1+2z2) and sinh-1(z)

>
>

Involving tanh-1(1+2z2/2 z (z2+1)1/2)

Involving tanh-1(1+2z2/2 z (z2+1)1/2) and sinh-1(z)

>
>
>
>
>