I'm not sure what the resolution is (the patch was 'inverse', Mark said 
he'd be happy to use 'area', and Raymond quoted 'arc').  I didn't know 
this would be a big deal, and I'm sorry that I caused trouble.  But 
since one of the concerns was divergence, I thought I'd send some info 
on how the tools I've used describe it -- universally as 'inverse' in 
those that I found:

- Mathematica: ArcCosh[z] "gives the inverse hyperbolic cosine [...]" 
(http://reference.wolfram.com/mathematica/ref/ArcCosh.html)
- Modelica Standard Library: acosh "Inverse of cosh (area hyperbolic 
cosine)" 
(http://reference.wolfram.com/system-modeler/libraries/Modelica/Modelica_Math_acosh.html)
- Maple: arccosh, but unknown description 
(http://www.maplesoft.com/support/help/Maple/view.aspx?path=invtrig)
- MATLAB: acosh " Inverse hyperbolic cosine" 
(http://www.mathworks.com/help/matlab/ref/acosh.html)
- TI-89 calculator: cosh-1 "returns the inverse hyperbolic cosine [...]" 
(from manual)

Respectfully,
Kevin