changing terminology (was: overview paper co-author invitation)

[Kouznetsov]

there is no 'arcsinh'

...

Interesting.

Nothing special. Not only Maple, but also C++ and Mathematica recognize arcsinh as inverse function of sinh. You may try also arccosh, arctanh, arcsech, etc.
Unfortunately, arcGamma is not yet implemented.

This is how I had envisioned the iterational terminology working:

• superfunction of F = iterational of F
  
• super-exponential = iter-exponential
  
• super-logarithm = inverse iter-exponential = Abel function of exponential
  
• super-F = iter-F
  

By using the "iter-" prefix instead of the "super-" prefix, there is no confusion with previous terminology, and we can continue using "super-logarithm" to mean what it has always meant. And to keep up with the current writings, I suppose these terms could be prefixed with mappings, like (0 -> 1) iter-cosine or something.

We already have the SuperFactorial and ArcSuperFactorial.
Should we rename them to Iter-factorial and Abel-factorial?

I see, Iter and Abel are couple, like integration and differentiation. Soon we may have also pen=pentational=(0 -> 1)Iter-tet, arcpen=ArcPentational=(1 -> 0)Abel-tet;
Iter-Bessel, Abel-Bessel; Abel-Mathieu; Abel-Legendre; Abel-(Hermit-Gaussian)...