Lambda function

This article is about the mathematical lambda function $\lambda (x,b)$ . For information about the computer science lambda function, see Lambda calculus. For the Dirichlet lambda function^[1], a Dirichlet L Series, see there.

In mathematics, 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.