U function

U(n) is an extremely fast-growing function devised by Chris Bird. It is the fastest function he defined as of June 2013. Its growth rate is around \(\theta(\Omega_\omega)\) in the fast-growing hierarchy.

Using Bird's Hierarchical Hyper-Nested Array Notation, \(U(n) = \{3,n [1 [1 [1 [ \cdots [1 [1 /_n 1 /_n 2] 2] \cdots ] 2] 2] 2] 2\}\) (with n sets of square brackets).