natural log base

The natural log base, or e, has value


e was extensively studied by Euler in the 1720’s, but it was originally discovered by John Napier.

e is defined by


It is more effectively calculated, however, by using the Taylor seriesMathworldPlanetmath for f(x)=ex at x=1 to get the representation

Title natural log base
Canonical name NaturalLogBase
Date of creation 2013-03-22 11:55:56
Last modified on 2013-03-22 11:55:56
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 11
Author CWoo (3771)
Entry type Definition
Classification msc 33B99
Synonym Euler numberDlmfDlmfMathworldPlanetmath
Synonym Eulerian numberDlmfMathworld
Synonym Napier’s constant
Synonym e
Related topic ExampleOfTaylorPolynomialsForTheExponentialFunction
Related topic EIsTranscendental
Related topic EIsIrrationalProof
Related topic ApplicationOfCauchyCriterionForConvergence