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ID: INPUT{id.yaml} Title: Euler's constant e Definition: > Euler's constant $e$ can be defined as the unique positive real number such that $e^x$ equals its own derivative. Parameters: Comments: Formulas: formula-series: > $e = \sum_{n\geq 0} 1/n!$. formula-limit: > $e = \lim_{n\to\infty} (1+1/n)^n$. formula-integral: > $\int_1^e 1/x\, dx = 1$. Programs: program-sage: language: Sage code: | numbers = [RBF(e)] References: Links: Wiki: title: "Wikipedia: e" url: https://en.wikipedia.org/wiki/E Similar tables: Keywords: Tags: - transcendental - irrational - exponential function Data properties: type: R Display properties: number-header: $e$ Numbers: - 2.718281828459045235360287471352662497757247093699959574966967627724076630353547594571382178525166427427466391932003059921817413596629043572900334295260595630738132328627943490763233829880753195251019011573834187930702154089149934884167509244761460668082264800168477411853742345442437107539077744992069
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Euler's constant e
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Numbers
$e$
2.718281828459045235360287471352662497757247093699959574966967627724076630353547594571382178525166427427466391932003059921817413596629043572900334295260595630738132328627943490763233829880753195251019011573834187930702154089149934884167509244761460668082264800168477411853742345442437107539077744992069
Definition
Euler's constant $e$ can be defined as the unique positive real number such that $e^x$ equals its own derivative.
Formulas
(1)
$e = \sum_{n\geq 0} 1/n!$.
(2)
$e = \lim_{n\to\infty} (1+1/n)^n$.
(3)
$\int_1^e 1/x\, dx = 1$.
Programs
(P1)
Sage
numbers = [RBF(e)]
Links
[1]
Wikipedia: e
Data properties
Entries are of type: real number