Euler-Mascheroni Constant (γ)

★★★★☆Undergraduate

📖Definition

The Euler-Mascheroni constant γ is the limit of the difference between harmonic series and natural log. Whether it's irrational is still unknown.

γ = lim_n → ∈fty ( ∑_k=1ⁿ (1)/(k) - ln n ) ≈ 0.5772...

Definition of Euler-Mascheroni constant

γ = ∈t₁^∈fty ( (1)/(⌊ x ⌋) - (1)/(x) ) dx

Integral representation

예제 1

Estimate the difference between H_100 and ln(100).

Discovered by: Leonhard Euler (1735)

Euler discovered it while studying the harmonic series.

Prime distribution

Gamma function

Extreme value distributions

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