Arrow notation or up-arrow notation is a widely used notation for the hyper operators, devised by Donald Knuth in 1976 to represent large numbers. It is defined by the following rules: \begin{eqnarray} a \uparrow^1 b &=& a^b \\ a \uparrow^n 1 &=& a \\ a \uparrow^{n + 1} (b + 1) &=& a \uparrow^n (a \uparrow^{n + 1} b) \\ \end{eqnarray} Specifically, \(a \uparrow b\) is exponentiation, \(a \uparrow\uparrow b\) is tetration, \(a \uparrow\uparrow\uparrow b\) is pentation, and so forth. In ASCII, these are written a^b, a^^b, a^^^b, ...