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 $\leq e$ .

References

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