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Template:Arsinh/doc
From OeisWiki
The {{arsinh}} (inverse) hyperbolic function template returns the inverse hyperbolic sine of , where is a real number.
Contents
Usage
- {{arsinh|a real number}}
Valid input
- A real number as argument.
Examples
Examples with valid input
Code Result {{arsinh|-1}} -0.88137358701954 {{arsinh|-0.5}} -0.4812118250596 {{arsinh|0}} 0 {{arsinh|0.5}} 0.4812118250596 {{arsinh|1}} 0.88137358701954 {{arsinh|{{sinh|-1}}}} -1 {{arsinh|{{sinh|-0.5}}}} -0.5 {{arsinh|{{sinh|0}}}} 0 {{arsinh|{{sinh|0.5}}}} 0.5 {{arsinh|{{sinh|1}}}} 1 {{arsinh|e^15 / 2}} 15 {{arsinh|e^-15 / 2}} 1.5295116003095E-7 {{arsinh|-(e^15) / 2}} -15 {{arsinh|-(e^-15) / 2}} -1.5295116003095E-7 {{arsinh|e^30 / 2}} 30 {{arsinh|e^-30 / 2}} 4.6851411639181E-14 {{arsinh|-(e^30) / 2}} -30 {{arsinh|-(e^-30) / 2}} -4.6851411639181E-14
Examples with invalid input (returns an error message)
Code Result {{arsinh|i}} Arsinh error: Argument must be a real number
Code
{{ifnum| {{{1|NAN}}} | {{#ifexpr: ({{{1}}}) >= 0 | {{#expr: ln ( ({{{1}}}) + ( ({{{1}}})^2 + 1 )^(1/2) ) }} | {{#expr: - ln ( - ({{{1}}}) + ( ({{{1}}})^2 + 1 )^(1/2) ) }} <!-- Equivalent, but avoids underflow for negative argument --> }} | {{error| Arsinh error: Argument must be a real number }} }}
See also