Difference between revisions of "Arccoth"

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The inverse hyperbolic cotangent $\mathrm{arccoth}$ is the [[inverse function]] of the [[coth|hyperbolic cotangent]] function. It may be defined in terms of the [[arctanh|inverse hyperbolic tangent]] function by the following formula:
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The inverse hyperbolic cotangent $\mathrm{arccoth}$ is the [[inverse function]] of the [[coth|hyperbolic cotangent]] function. It may be defined by the following formula:
$$\mathrm{arccoth}(z)=\mathrm{arctanh} \left( \dfrac{1}{z} \right).$$
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$$\mathrm{arccoth}(z)=\mathrm{arctanh} \left( \dfrac{1}{z} \right),$$
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where $\mathrm{arctanh}$ denotes the [[arctanh|inverse hyperbolic tangent]].
  
 
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==Properties==
 
==Properties==
 
[[Derivative of arccoth]]<br />
 
[[Derivative of arccoth]]<br />
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==See also==
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[[Arccot]] <br />
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[[Cotangent]]<br />
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[[Coth]]<br />
  
 
{{:Inverse hyperbolic trigonometric functions footer}}
 
{{:Inverse hyperbolic trigonometric functions footer}}
  
 
[[Category:SpecialFunction]]
 
[[Category:SpecialFunction]]

Latest revision as of 01:40, 16 September 2016

The inverse hyperbolic cotangent $\mathrm{arccoth}$ is the inverse function of the hyperbolic cotangent function. It may be defined by the following formula: $$\mathrm{arccoth}(z)=\mathrm{arctanh} \left( \dfrac{1}{z} \right),$$ where $\mathrm{arctanh}$ denotes the inverse hyperbolic tangent.

Properties

Derivative of arccoth

See also

Arccot
Cotangent
Coth

Inverse hyperbolic trigonometric functions