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Down Arrow Notation

An inverse of the up Arrow Notation defined by

$\displaystyle e\downarrow n$ $\textstyle =$ $\displaystyle \ln n$  
$\displaystyle e\downarrow \downarrow n$ $\textstyle =$ $\displaystyle \ln^* n$  
$\displaystyle e\downarrow \downarrow \downarrow n$ $\textstyle =$ $\displaystyle \ln^{**} n,$  

where $\ln^* n$ is the number of times the Natural Logarithm must be iterated to obtain a value $\leq e$.

See also Arrow Notation


Vardi, I. Computational Recreations in Mathematica. Redwood City, CA: Addison-Wesley, pp. 12 and 231-232, 1991.

© 1996-9 Eric W. Weisstein