Euler's constant e
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Number
$e$
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
Data properties
Numbers are of type: real number