# The Repeated Power Function

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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

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"The Repeated Power Function"

http://demonstrations.wolfram.com/TheRepeatedPowerFunction/

Wolfram Demonstrations Project

Published: March 7 2011