Difference between revisions of "Tanh"

From specialfunctionswiki
Jump to: navigation, search
 
Line 26: Line 26:
 
[[Halving identity for tangent (2)]]<br />
 
[[Halving identity for tangent (2)]]<br />
 
[[Halving identity for tangent (3)]]<br />
 
[[Halving identity for tangent (3)]]<br />
 +
[[Doubling identity for sinh (2)]]<br />
  
 
=See Also=
 
=See Also=

Latest revision as of 23:43, 21 October 2017

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.

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
Pythagorean identity for tanh and sech
Period of tanh
Tanh is odd
Tanh of a sum
Halving identity for tangent (1)
Halving identity for tangent (2)
Halving identity for tangent (3)
Doubling identity for sinh (2)

See Also

Arctan
Arctanh
Tangent

References

Hyperbolic trigonometric functions