Lambda function

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This article is about the mathematical lambda function. For information about the computer science lambda function, see Lambda calculus.[1]

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

[edit] References

  1. ^ Lambda Function (Wolfram MathWorld)
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