Difference between revisions of "Tanh"

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[[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 />
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[[Pythagorean identity for tanh and sech]]<br />
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[[Period of tanh]]<br />
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[[Tanh is odd]]<br />
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[[Tanh of a sum]]<br />
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[[Halving identity for tangent (1)]]<br />
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[[Halving identity for tangent (2)]]<br />
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[[Halving identity for tangent (3)]]<br />
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[[Doubling identity for sinh (2)]]<br />
  
 
=See Also=
 
=See Also=
[[Arctanh]]
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[[Arctan]]<br />
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[[Arctanh]]<br />
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[[Tangent]]<br />
  
<center>{{:Hyperbolic trigonometric functions footer}}</center>
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=References=
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* {{BookReference|Handbook of mathematical functions|1964|Milton Abramowitz|author2=Irene A. Stegun|prev=Cosh|next=Csch}}: $4.5.3$
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{{:Hyperbolic trigonometric functions footer}}
  
 
[[Category:SpecialFunction]]
 
[[Category:SpecialFunction]]

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