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# ArcSinh

 ArcSinh[z]gives the inverse hyperbolic sine of the complex number .
• Mathematical function, suitable for both symbolic and numerical manipulation.
• For certain special arguments, ArcSinh automatically evaluates to exact values.
• ArcSinh can be evaluated to arbitrary numerical precision.
• ArcSinh automatically threads over lists.
• ArcSinh[z] has branch cut discontinuities in the complex plane running from to and to .
Evaluate numerically:
Series expansion:
 Scope   (6)
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
ArcSinh threads element-wise over lists:
Simple exact values are generated automatically:
Parity transformation is automatically applied:
ArcSinh can be applied to a power series:
ArcSinh can deal with real-valued intervals:
Infinite arguments generate exact results:
 Applications   (2)
Compute the length of hyperbola from the base to given x:
Solve a differential equation:
Compose with the inverse function:
Use PowerExpand to disregard multivaluedness of the ArcSinh:
Alternatively, evaluate under additional assumptions:
Use TrigToExp to express ArcSinh using logarithm:
Use Reduce to solve an equation in terms of ArcSinh:
ArcSinh is a special case of some special functions:
Integrals:
Generically :
When using input in traditional form, parentheses are needed around the argument:
Compute 100,000 digits of , and show the first and last 20 digits:
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