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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][dead link]

## Examples

• $$h_3(2,6) = 2 \uparrow 6$$
• $$h_3(10,100) = 10 \uparrow 100$$ (googol)
• $$h_4(10,100) = 10 \uparrow\uparrow 100$$ (giggol)
• $$h_5(10,100) = 10 \uparrow\uparrow\uparrow 100$$ (gaggol)
• $$h_4(2,6,2) = h_{h_4(2,5)}(2,6) = h_{2\uparrow^6 5}(2,6) = 2 \uparrow^{2 \uparrow^{6} 5-2} 6$$

## 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, which is closely related to the expansion function ({x,x,1,2}). The two-entry hyperlicious function ($$h_x(a,b)$$) eventually dominates any hyper-operator, such as tetration, pentation, or even beyond centation.