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单词 NaturalLogBase
释义

natural log base


The natural log base, or e, has value

2.718281828459045

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

e is defined by

limn(1+1n)n

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

e=10!+11!+12!+13!+14!+
Titlenatural log base
Canonical nameNaturalLogBase
Date of creation2013-03-22 11:55:56
Last modified on2013-03-22 11:55:56
OwnerCWoo (3771)
Last modified byCWoo (3771)
Numerical id11
AuthorCWoo (3771)
Entry typeDefinition
Classificationmsc 33B99
SynonymEuler numberDlmfDlmfMathworldPlanetmath
SynonymEulerian numberDlmfMathworld
SynonymNapier’s constant
Synonyme
Related topicExampleOfTaylorPolynomialsForTheExponentialFunction
Related topicEIsTranscendental
Related topicEIsIrrationalProof
Related topicApplicationOfCauchyCriterionForConvergence
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更新时间:2025/5/4 14:05:12