The Repeated Power Function

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

Leonhard Euler proved that the function , where appears times, approaches a limit for as . (The red points indicate the limits at the endpoints of the interval of convergence.) This Demonstration shows the values of for to . You can zoom in to see the limits at and . The expression bifurcates at the lower endpoint () with . The sequence converges to 1 as from above while converges to 0. Beyond the upper endpoint () the expression rapidly grows to infinity.

Contributed by: Bill Collins (March 2011)
Open content licensed under CC BY-NC-SA




Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.