# Closed-Form Approximations of Euler's Number *e*

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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 .

Contributed by: Sakethnath Are (January 2012)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

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.

## Permanent Citation