Super-root

In mathematics, the super-root is one of the two inverse functions of tetration. Just as exponentiation has two inverse functions: roots and logarithms, likewise tetration has two inverse functions: super-roots and super-logarithms. The super-root is the inverse function of tetration with respect to the base: if ^n y = x, then "y" is an "n"th super root of "x".

Square root

The 2nd-order super-root, or "super square root", is noteworthy for its simple expression in terms of Lambert's W function. Namely,

:ssqrt(x) = e^{mathrm{W}(mathrm{ln}(x))}

ee also

*Hyper operator


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