La fonsion d'Ackermann A c k : N 2 → N {\displaystyle Ack:\mathbb {N} ^{2}\rightarrow \mathbb {N} } a l'é la fonsion definìa 'd fasson arcorsiva da
A c k ( n , m ) = { m + 1 si n = 0 A c k ( n − 1 , 1 ) si m = 0 , n ≥ 1 A c k ( n − 1 , A c k ( n , m − 1 ) ) si m ≥ 1 , n ≥ 1. {\displaystyle Ack(n,m)=\left\{{\begin{array}{ll}m+1&{\mbox{si }}n=0\\Ack(n-1,1)&{\mbox{si }}m=0,n\geq 1\\Ack(n-1,Ack(n,m-1))&{\mbox{si }}m\geq 1,n\geq 1.\end{array}}\right.}