Euler-Mascheroni constant
The Euler-Mascheroni constant is a mathematical constant, used mainly in number theory, and is defined as the limiting difference between the harmonic series and the natural logarithm:
Intriguingly, the constant is also given by the integral:
Its value is approximately
- γ ≈ 0.577215664901532860606512090082402431042159335 9399235988057672348848677267776646709369470632917467495...
It is not known whether γ is a rational number or not. However, continued fraction analysis shows that if γ is rational, its denominator has more than 10,000 digits.
The Euler-Mascheroni constant appears, among other places, in:
External link
Euler-Mascheroni constant
Referenced By
Cosine integral | Digamma function | EuleR | Franz Mertens | Gamma | Gamma (letter) | Gamma function | Harmonic number | Harmonic series (mathematics) | Hyperbolic cosine integral | Hyperbolic sine integral | Khinchin's constant | Leonard Euler | LeonhardEuler | Leonhard Euler | Letters used in Maths and Science | List of letters used in mathematics and science | List of mathematical topics (D-F) | List of mathematical topics (F-Z) | List of numbers | Lorenzo Mascheroni | Mathematical constant | Mathematical constant/Alternative sorting | Mathematical constant (sorted by continued fraction representation) | Mathematical constants | Meissel-Mertens constant | Merten's conjecture | Pi function | Proof that the sum of the reciprocals of the primes diverges | Sine integral | Trigonometric integral | Trigonometric integrals
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