Recursion in the Ackermann Function

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The Ackermann function is a classic example of a function that is not "primitive recursive"—its evaluation cannot be "unwound" into simple loops. See how instances of the Ackermann function get evaluated by calling on others. The Ackermann function grows very rapidly. As its first argument increases, it effectively goes from addition, to multiplication, powers, power towers, etc.

Contributed by: Stephen Wolfram (March 2011)
Open content licensed under CC BY-NC-SA



The definition used here is

which is a slight modification of Wilhelm Ackermann's original 1926 function.

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