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Template:Artanh/doc
From OeisWiki
The {{artanh}} (inverse) hyperbolic function template returns the inverse hyperbolic tangent of , where is a real number.
Contents
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 error: Argument must be a real number in open interval (-1, +1) {{artanh|-5}} Artanh error: Argument must be a real number in open interval (-1, +1) {{artanh|-2}} Artanh error: Argument must be a real number in open interval (-1, +1) {{artanh|-1}} Artanh error: Argument must be a real number in open interval (-1, +1) {{artanh|1}} Artanh error: Argument must be a real number in open interval (-1, +1) {{artanh|2}} Artanh error: Argument must be a real number in open interval (-1, +1) {{artanh|5}} Artanh error: Argument must be a real number in open interval (-1, +1)
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