Re: ArcTanh[x,y] & Wikipedia.

Macsyma / Maxima uses  asin   and asinh   (etc.)

I would not expect the openmath standard to be held up
as an example to be followed; rather the openmath people
seem to try to follow someone else's standard. e.g. what
does "cos" mean?  Well, what it usually means.

I also would not want Mathematica to become a standard
setter because it sometimes differs from the previous
convention for no reason I can see.  For example,
I think reversing the arguments of arctan2 from convention.
[not the arctanh2 of the subject line]

RJF



David N. Williams wrote:

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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