The Repeated Power Function
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
Snapshots
Details
detailSectionParagraphPermanent Citation
"The Repeated Power Function"
http://demonstrations.wolfram.com/TheRepeatedPowerFunction/
Wolfram Demonstrations Project
Published: March 7 2011