Lambda Function

The Lambda Function is a type of exponential function, where a number, x, is raised to itself, raised to (b−1):
:

\lambda(x,b) = x^{x^{b-1}}

Sending b to infinity causes the function to approach 1 for x < 1, and infinity for x > 1. It can be thought of as an iterated exponential function:

\lambda(x,b) = x^{x^{x^{\dots}}}

, where there are b levels of exponentiation, associated from the bottom up.

See also: Tetration

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