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, 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.

See also

• Tetration

References

• Weisstein, Eric W. "Lambda Function". MathWorld.