Euler's constant
Constant value used in mathematics / From Wikipedia, the free encyclopedia
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Not to be confused with Euler's number, e ≈ 2.71828, the base of the natural logarithm.
Euler's constant (sometimes called the Euler–Mascheroni constant) is a mathematical constant, usually denoted by the lowercase Greek letter gamma (γ), defined as the limiting difference between the harmonic series and the natural logarithm, denoted here by log:
This article uses technical mathematical notation for logarithms. All instances of log(x) without a subscript base should be interpreted as a natural logarithm, also commonly written as ln(x) or loge(x).
Quick Facts 's constant, General information ...
Euler's constant | |
---|---|
γ 0.57721...[1] | |
General information | |
Type | Unknown |
Fields | |
History | |
Discovered | 1734 |
By | Leonhard Euler |
First mention | De Progressionibus harmonicis observationes |
Named after |
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Here, ⌊·⌋ represents the floor function.
The numerical value of Euler's constant, to 50 decimal places, is:[1]
0.57721566490153286060651209008240243104215933593992...
Unsolved problem in mathematics:
Is Euler's constant irrational? If so, is it transcendental?