This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# Tanh

 Tanh[z]gives the hyperbolic tangent of .
• Mathematical function, suitable for both symbolic and numerical manipulation.
• For certain special arguments, Tanh automatically evaluates to exact values.
• Tanh can be evaluated to arbitrary numerical precision.
• Tanh automatically threads over lists.
Evaluate numerically:
Evaluate numerically:
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 Scope   (11)
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Tanh threads element-wise over lists and matrices:
Tanh can take complex number inputs:
Simple exact purely imaginary values are generated automatically:
Convert multiple-angle expressions:
Find factors of decomposition:
Convert sums of hyperbolic functions to products:
Expand assuming real variables:
Convert to exponentials:
Tanh can deal with real-valued intervals:
Infinite arguments give symbolic results:
Tanh can be applied to power series:
 Applications   (4)
Plot a tractrix pursuit curve:
Plot a pseudosphere:
Calculate the finite area of the surface extending to infinity:
Velocity of a relativistic body in a constant force field:
Solution of the Burgers' equation using the tanh method:
Basic parity and periodicity properties of Tanh are automatically applied:
Expressions containing hyperbolic functions do not automatically simplify:
Use Refine, Simplify, and FullSimplify to simplify expressions containing Tanh:
Use FunctionExpand to express special values in radicals:
Compose with inverse functions:
Solve a hyperbolic equation:
Numerically find a root of a transcendental equation:
Reduce a hyperbolic equation:
Integrals:
Integral transforms:
Obtain Tanh from sums and integrals:
Tanh appears in special cases of special functions:
Tanh is a numeric function:
Machine-precision input is insufficient to give a correct answer:
With exact input, the answer is correct:
A larger setting for \$MaxExtraPrecision can be needed:
No power series exists at infinity, where Tanh has an essential singularity:
In traditional form parentheses are needed around the argument:
Continued fraction expansion: