Hyperoperation - Notations

Notations

This is a list of notations that have been used for hyperoperations.

Name	Notation equivalent to	Comment
Knuth's up-arrow notation		Used by Knuth (for n ≥ 2), and found in several reference books.
Goodstein's notation		Used by Reuben Goodstein.
Original Ackermann function	$\begin{matrix} \phi(a, b, n-1) \ \text{ for } 1 \le n \le 3 \\ \phi(a, b-1, n-1) \ \text{ for } n > 3 \end{matrix}\,\!$	Used by Wilhelm Ackermann.
Ackermann–Péter function		This corresponds to hyperoperations for base 2.
Nambiar's notation		Used by Nambiar
Box notation		Used by Rubtsov and Romerio.
Superscript notation		Used by Robert Munafo.
Subscript notation		Used for lower hyperoperations by Robert Munafo.
Square bracket notation		Used in many online forums; convenient for ASCII.

Read more about this topic: Hyperoperation