Difference between revisions of "Tanh"
From specialfunctionswiki
| Line 19: | Line 19: | ||
[[Relationship between tanh, inverse Gudermannian, and sin]]<br /> | [[Relationship between tanh, inverse Gudermannian, and sin]]<br /> | ||
[[Taylor series for Gudermannian]]<br /> | [[Taylor series for Gudermannian]]<br /> | ||
| + | [[Period of tanh]]<br /> | ||
=See Also= | =See Also= | ||
Revision as of 18:16, 7 August 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
Period of tanh
See Also
References
- 1964: Milton Abramowitz and Irene A. Stegun: Handbook of mathematical functions ... (previous) ... (next): 4.5.3
