Re: ArcTanh[x,y] & Wikipedia.

Simo K Kivelä wrote:

"Roger Beresford" <mail@xxxxxxxxxxxxxxxxxxxxxxxxxxx> writes:


When I added the definition ArcTanh[x,y]:=Log[(x+y)/SQRT[x^2-y^2]] (due 


By the way, the names of the inverse hyperbolic functions should be
arsinh, arcosh, artanh etc. and not arc*. The latin names of the functions
are 'area sinus hyperbolicus' etc. where 'area' refers to the area of a
sector bounded by the unit hyperbola. In the trigonometric case, 'arc' is
correct because the value of the function represents the length of an arc.
(It could also be considered as area of a sector and therefore, 'ar' would
in principle be correct also here, but it has never been used.) In the
hyperbolic case, there is no arc, and the use of 'arc' should be considered
as a mistake.


A mistake in that sense, but "arc" has very wide usage.  And
it's standardized in the open math standard, e.g.,

  http://www.openmath.org/cocoon/openmath/cd/transc3.html#arctanh

I believe their case for standardizing such things, including
the definitions of principal branches, is compelling.

-- David

.

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