08/06/2009, 02:36 AM

(08/05/2009, 06:15 PM)bo198214 Wrote: .. the "arc" prefix for trigonometric functions comes from measuring the length of the arc on the unit circle (which is the angle).How about arcsinh, arccosh,..? Now the prefix "arc" means "inverse function of".

So etymologically this would count against a usage as "inverse"-prefix.

If I ask for "ArcGamma", everybody understands what do I mean, but if I say "inverse of Gamma", the GNU offers f(z)=1/Gamma(z) instead.

I know that slog already appears in some texts as inverse of tetrational; sorry about that. But I do not extend this confusion to the new texts.

I suggest the rule: if there is some holomorphic function Func, then

the inverse is called ArcFunc,

the superfunction of Func is called SuperFunc,

and its inverse function is called ArcSuperFunc.

For example, if a superfunction of tetrational, we already have names for it:

pentational=pen=SuperTetrational

and its inverse should be called arcpen=ArcSuperTetrational

We need two prefices to indicate the inverse function and to indicate the superfincton.

"arc" and "super" are best.