Definition:Hyperoperation/Nth Hyperoperation
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Definition
Let $\left\langle{H_n}\right\rangle$ denote the hyperoperation sequence.
The $n$th term of $\left\langle{H_n}\right\rangle$, which is the binary operation $H_n : \Z_{\ge 0} \times \Z_{\ge 0} \to \Z_{\ge 0}$, is known as the $n$th hyperoperation.
$\forall x, y \in \Z_{\ge 0}: H_n \left({x, y}\right) = \begin{cases}
y + 1 & : n = 0 \\
x & : n = 1, y = 0 \\
0 & : n = 2, y = 0 \\
1 & : n > 2, y = 0 \\
H_{n - 1} \left({x, H_n \left({x, y - 1}\right)}\right) & : n > 0, y > 0 \end{cases}$
Also known as
Some sources refer to a hyperoperation as a hyperoperator function.