Re: [Patch, Fortran, Doc] Inverse hyperbolic functions

[bd satish <bdsatish at gmail dot com>]

Hi there !

In India, we learn them as "inverse hyperbolic functions".  Frankly,
the name "hyperbolic area tangent" is quite strange to me; it's the
first time I'm hearing it !

-- Satish.BD



On Sun, Aug 8, 2010 at 11:25 PM, Janus Weil <janus@gcc.gnu.org> wrote:
> Hi Dominique,
>
>> I agree that "Inverse hyperbolic *" is better than "Hyperbolic arc*"
>> (when I was taught hyperbolic functions and their inverses some 45 years
>> ago, they were denoted ch, sh, and th and the inverses argch, argsh,
>> and argth, I have no idea about the today fashion!-).
>>
>> However the inverse hyperbolic functions appear in many places and
>> not in non-Euclidian geometry only, so I am not very fond
>> (to say the least) of "hyperbolic area". Why not
>> "computes the inverse @var{X} of the hyperbolic * (@code{*(X)})."
>> (or any suitable translation from Frenglish to native English!).
>
> well, I'm starting to think that there may be regional differences in
> the naming of the inverse hyperbolics (though I'm not sure about
> this)?
>
> The common naming convention in Germany, I think, is that the inverse
> trigonometrics are called ARCTAN etc, while in contrast the inverse
> hyperbolics are labeled ATANH or ARTANH, where the 'A' or 'AR' in
> front stands for 'area' (and not for 'arc'). This is confirmed by my
> copy of the Mathematical Handbook by Bronstein et al. (which I think
> is Russian by origin), and which even goes into some depth to explain
> where this naming comes from.
>
> However, I just had a look into Abramowitz & Stegun, which has
> ARCTANH, cf. http://www.math.ucla.edu/~cbm/aands/page_86.htm
>
> So maybe it is indeed common to talk about an 'hyperbolic arctangent"
> in the US (and France?). What is the ultimate mathematical instance
> than we should follow? Maybe it is best to stick to the neutral
> "inverse hyperbolic tangent"? Or should we rather mention both naming
> conventions in the manual?
>
> Cheers,
> Janus
>