Euler–Mascheroni constant γ

All labels observed (4)

Label	Occurrences
Euler constant	1
Euler–Mascheroni constant	1
Euler–Mascheroni constant γ canonical	1
Mascheroni constant	1

How this entity was disambiguated

This entity first appeared as the object of triple T6482593 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Euler–Mascheroni constant γ
Context triple: [Gamma function, containsConstant, Euler–Mascheroni constant γ]

A. Gauss’s constant
Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
B. Khinchin's constant
Khinchin's constant is a mathematical constant that arises in metric number theory, describing the almost-sure geometric mean of the partial quotients in the continued fraction expansions of real numbers.
C. Gamma function
The Gamma function is a fundamental extension of the factorial function to complex and real non-integer arguments, widely used in analysis, probability, and mathematical physics.
D. Khinchin–Lévy constant
The Khinchin–Lévy constant is a mathematical constant arising in metric number theory and continued fractions, describing the typical exponential growth rate of the denominators of convergents for almost all real numbers.
E. Pi
Pi is a 1998 psychological thriller film directed by Darren Aronofsky that explores obsession, mathematics, and mysticism through the story of a reclusive number theorist.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Euler–Mascheroni constant γ
Target entity description: The Euler–Mascheroni constant γ is a mathematical constant that arises in analysis and number theory, defined as the limiting difference between the harmonic series and the natural logarithm.

A. Gauss’s constant
Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
B. Khinchin's constant
Khinchin's constant is a mathematical constant that arises in metric number theory, describing the almost-sure geometric mean of the partial quotients in the continued fraction expansions of real numbers.
C. Gamma function
The Gamma function is a fundamental extension of the factorial function to complex and real non-integer arguments, widely used in analysis, probability, and mathematical physics.
D. Khinchin–Lévy constant
The Khinchin–Lévy constant is a mathematical constant arising in metric number theory and continued fractions, describing the typical exponential growth rate of the denominators of convergents for almost all real numbers.
E. Pi
Pi is a 1998 psychological thriller film directed by Darren Aronofsky that explores obsession, mathematics, and mysticism through the story of a reclusive number theorist.
F. None of above. chosen

Statements (48)

Predicate	Object
instanceOf	mathematical constant ⓘ
alternativeName	Euler constant ⓘ linked to: Euler–Mascheroni constant γ Mascheroni constant ⓘ linked to: Euler–Mascheroni constant γ
appearsIn	analysis ⓘ analytic number theory ⓘ asymptotic analysis of harmonic numbers ⓘ number theory ⓘ special functions ⓘ
approximateDecimalExpansion	0.57721566490153286060651209008240243104215933593992… ⓘ
approximateValue	0.57721 ⓘ 0.5772156649 ⓘ
conjecturedProperty	believed to be irrational ⓘ believed to be transcendental ⓘ
definition	lim_{n→∞}(1 + 1/2 + 1/3 + … + 1/n − ln n) ⓘ
discoveredBy	Leonhard Euler ⓘ
domain	analytic number theory ⓘ real analysis ⓘ
historicalNote	further investigated by Lorenzo Mascheroni ⓘ studied by Euler in the 18th century ⓘ
integralRepresentation	γ = ∫_0^1 (1 − H_x) dx where H_x is analytically continued ⓘ γ = ∫_0^∞ (e^{−x}/x − e^{−x}/(1 − e^{−x})) dx ⓘ
namedAfter	Leonhard Euler ⓘ Lorenzo Mascheroni ⓘ
openProblem	It is unknown whether γ is algebraic or transcendental ⓘ It is unknown whether γ is rational or irrational ⓘ
relation	H_n = ln n + γ + 1/(2n) + O(1/n^2) ⓘ H_n = ln n + γ + o(1) as n→∞ ⓘ appears in Mertens' theorems ⓘ appears in estimates for the average order of arithmetic functions ⓘ appears in the Laurent expansion of ζ(s) at s = 1 ⓘ appears in the asymptotic expansion of the factorial via Γ function ⓘ appears in the constant term of many asymptotic expansions involving logarithms ⓘ ln n! = n ln n − n + (1/2) ln(2πn) + γ/(12n) + O(1/n^3) ⓘ Γ'(1) = −γ ⓘ γ = lim_{n→∞}(H_n − ln n) ⓘ γ = lim_{n→∞}(∑_{k=1}^n 1/k − ln n) ⓘ γ = −Γ'(1) ⓘ γ = −ψ(1) ⓘ γ = ∫_0^1 (1 − 1/ln x) dx is incorrect (divergent integral) ⓘ γ = ∫_1^∞ (1/⌊x⌋ − 1/x) dx ⓘ ζ(s) = 1/(s − 1) + γ + O(s − 1) as s→1 ⓘ ψ(x) = d/dx ln Γ(x) and ψ(1) = −γ ⓘ ∏_{p≤x} (1 − 1/p) ∼ e^{−γ}/ln x as x→∞ ⓘ ∑_{p≤x} 1/p = ln ln x + B_1 + o(1) where B_1 is related to γ ⓘ
seriesRepresentation	γ = 1 − ln 2 + ∑_{n=2}^∞ (−1)^n (ζ(n)/n) ⓘ γ = ∑_{n=1}^∞ (1/n − ln((n+1)/n)) ⓘ γ = ∑_{n=2}^∞ (−1)^n ζ(n)/n ⓘ
symbol	γ ⓘ