Template:Artanh/doc

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The {{artanh}} (inverse) hyperbolic function template returns the inverse hyperbolic tangent of $\scriptstyle x\,$, where $\scriptstyle x,\,|x|\,<\,1,\,$ is a real number.

Usage

{{artanh|a real number in open interval (-1, +1)}}

Valid input

A real number in open interval (-1, +1) as argument.

Examples

Examples with valid input

Code	Result
{{artanh|-0.95}}	-1.8317808230648
{{artanh|-0.5}}	-0.54930614433405
{{artanh|-0.3}}	-0.30951960420311
{{artanh|0}}	0
{{artanh|0.3}}	0.30951960420311
{{artanh|0.5}}	0.54930614433405
{{artanh|0.95}}	1.8317808230648
{{artanh|{{tanh|-1}}}}	-0.99999999999999
{{artanh|{{tanh|-0.5}}}}	-0.5
{{artanh|{{tanh|0}}}}	0
{{artanh|{{tanh|0.5}}}}	0.5
{{artanh|{{tanh|1}}}}	0.99999999999999

Examples with invalid input (returns an error message)

Code	Result
{{artanh|i}}
{{artanh|-5}}
{{artanh|-2}}
{{artanh|-1}}
{{artanh|1}}
{{artanh|2}}
{{artanh|5}}

Code

{{ifnum| {{{1|not a number}}}
| {{#ifexpr: abs ({{{1}}}) < 1
  | {{#expr: ( ln ( (1 + ({{{1}}})) / (1 - ({{{1}}})) ) ) / 2 }}
  | {{error| Artanh error: Argument must be a real number in open interval (-1, +1) }}
  }}
| {{error| Artanh error: Argument must be a real number in open interval (-1, +1) }}
}}

See also

• Hyperbolic functions
• Inverse hyperbolic functions

• {{sinh}}
• {{cosh}}
• {{tanh}}

• {{csch}}
• {{sech}}
• {{coth}}

• {{arsinh}} (see also {{qlog}})
• {{arcosh}}
• {{artanh}}

• {{arcsch}}
• {{arsech}}
• {{arcoth}}