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 .

[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.