Difference between revisions of "Tanh"
From specialfunctionswiki
| Line 22: | Line 22: | ||
=See Also= | =See Also= | ||
[[Arctanh]] | [[Arctanh]] | ||
| + | |||
| + | =References= | ||
| + | * {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Cosh|next=Csch}}: 4.5.3 | ||
<center>{{:Hyperbolic trigonometric functions footer}}</center> | <center>{{:Hyperbolic trigonometric functions footer}}</center> | ||
[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Revision as of 21:59, 21 June 2016
The hyperbolic tangent is defined by the formula $$\mathrm{tanh}(z)=\dfrac{\mathrm{sinh}(z)}{\mathrm{cosh}(z)},$$ where $\mathrm{sinh}$ is the hyperbolic sine and $\mathrm{cosh}$ is the hyperbolic cosine.
Plot of $\mathrm{tanh}$ on $[-5,5]$.
Domain coloring of $\tanh$.
Properties
Derivative of tanh
Antiderivative of tanh
Relationship between tanh and tan
Relationship between tan and tanh
Relationship between sine, Gudermannian, and tanh
Relationship between tanh, inverse Gudermannian, and sin
Taylor series for Gudermannian
See Also
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 4.5.3
