nested logarithm - Wolfram|Alpha

Uh oh! Wolfram|Alpha doesn't run without JavaScript.

Please enable JavaScript. If you don't know how, you can find instructionshere.Once you've done that, refresh this page to start using Wolfram|Alpha.

Input interpretation

nested logarithm

Alternate names

iterated logarithm | repeated logarithm

Definition

In number theory, the symbol log_k x is commonly used to mean the nested logarithm (also called the repeated logarithm or iterated logarithm) ln...ln_︸_k x, where ln x is the natural logarithm.
Care must be taken based on context as to when the notation log_k x denotes the logarithm to base k and when it means the k-nested natural logarithm.
The plots above show ln z, ln ln z, and ln ln ln z in the complex plane.
The penchant for formulas and bounds containing a profusion of nested logarithms has led to the following joke. What sound does a drowning analytic number theorist make? A: log log log log....

More information »

Related terms

binary logarithm | common logarithm | logarithm | natural logarithm

Subject classifications

MathWorld

logarithms

MSC 2010

33B10 | 33B30

POWERED BY THE WOLFRAM LANGUAGE

Related Queries:

Have a question about using Wolfram|Alpha?Contact Pro Premium Expert Support »

Give us your feedback »