9853

Closed-Form Approximations of Euler's Number e

There are many different closed-form expressions for Euler's number . All are functions such that approaches as approaches infinity. However, each expression exhibits a different rate of convergence. This Demonstration offers a visual representation of the behavior of these functions at smaller values of .

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Methods
classical:
complementary classical:
complementary addition (CAM):
mirror image (MIM):
power ratio (PRM):
CAM-MIM-PRM amalgam:
Brothers–Knox:
Reference
[1] H. J. Brothers and J. A. Knox, "New Closed-Form Approximations to the Logarithmic Constant e," The Mathematical Intelligencer, 20(4), 1998 pp. 25–29.

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