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Euler-Mascheroni Constant

Decimal approximation

0.57721566490153286060651209008240243104215933593992359880576723488486772677...

Number line

Continued fraction

[0; 1, 1, 2, 1, 2, 1, 4, 3, 13, 5, 1, 1, 8, 1, 2, 4, 1, 1, 40, 1, 11, 3, 7, 1, 7, 1, 1, 5, 1, 4, ...]

Alternative representation

gamma = γ_0

gamma = -ψ(1)

Series representation

gamma = sum_(k=1)^∞(1/k - log((k + 1)/k))

gamma = 1 + sum_(k=2)^∞(1/k + log(1 - 1/k))

gamma = sum_(k=2)^∞ (ζ(k) (-1)^k)/k

Integral representation

gamma = - integral_0^1 log(-log(t)) dt

gamma = - integral_(-∞)^∞ t e^(t - e^t) dt

gamma = - integral_0^∞ log(t)/e^t dt