This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# ArcCosh

 ArcCosh[z]gives the inverse hyperbolic cosine of the complex number .
• Mathematical function, suitable for both symbolic and numerical manipulation.
• For certain special arguments, ArcCosh automatically evaluates to exact values.
• ArcCosh can be evaluated to arbitrary numerical precision.
• ArcCosh automatically threads over lists.
• ArcCosh[z] has a branch cut discontinuity in the complex plane running from to .
Evaluate numerically:
Series expansion:
Evaluate numerically:
 Out[1]=
 Out[2]=

 Out[1]=

Series expansion:
 Out[1]=
 Scope   (6)
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Simple exact purely imaginary values are generated automatically:
Convert to logarithm:
ArcCosh can deal with real-valued intervals from :
Infinite arguments give symbolic results:
ArcCosh can be applied to power series:
 Applications   (3)
Find the rapidity of a boost that makes the energy of a body twice its rest energy:
Fraction of the speed of light required:
Width at the base of the inverted catenary arch of Gateway Arch in St. Louis, Missouri, in feet:
Plot the real and imaginary part of ArcCosh:
Compositions with the inverse function might need PowerExpand to simplify to an identity: