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The hyperlicious function is defined as

  • \(h_x(a,b) = a\uparrow^{x-2} b \),
  • \(h_x(a,b,c,\ldots,m,n,1) = h_x(a,b,c,\ldots,m,n)\), and
  • \(h_x(a,b,c,\ldots,m,n) = h_{h_x(a,b,c,\ldots,m - 1)}(a,b,c,\ldots,m)\).[1]

Examples

\(h_3(2,6) = 2 \uparrow 6\)

\(h_4(2,6,2) = h_{h_4(2,5)}(2,6) = h_{2\uparrow^6 5}(2,6) = 2 \uparrow^{2 \uparrow^{6} 5-2} 6\)

Growth rate

\(h(x) = h_x(x,x...x,x)\) with x x's in the array is approximately \(f_{\omega+1}(x)\) in the fast growing hierarchy

Sources

See also

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