Template:Arsinh/doc

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The {{arsinh}} (inverse) hyperbolic function template returns the inverse hyperbolic sine of $\scriptstyle x\,$, where $\scriptstyle x\,$ is a real number.

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}}

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

• Hyperbolic functions
• Inverse hyperbolic functions

• {{sinh}}
• {{cosh}}
• {{tanh}}

• {{csch}}
• {{sech}}
• {{coth}}

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

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