Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site ContributeEmail CommentsSign the Guestbook

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

Download All Introductions For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











Tanh






Mathematica Notation

Traditional Notation









Elementary Functions > Tanh[z] > Introduction to the Hyperbolic Tangent Function





Representation through more general functions


The hyperbolic tangent function can be represented using more general mathematical functions. As the ratio of the hyperbolic sine and cosine functions that are particular cases of the generalized hypergeometric, Bessel, Struve, and Mathieu functions, the hyperbolic tangent function can also be represented as ratios of those special functions. But these representations are not very useful. It is more useful to write the hyperbolic tangent function as particular cases of one special function. That can be done using doubly periodic Jacobi elliptic functions that degenerate into the hyperbolic tangent function when their second parameter is equal to or :





© 1998- Wolfram Research, Inc.