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Meissel-Mertens constant

The Meissel–Mertens constant (named after Ernst Meissel and Franz Mertens), also referred to as Mertens constant, Kronecker's constant, Hadamard–de la Vallée-Poussin constant or the prime reciprocal constant, is a mathematical constant in number theory, defined as the limiting difference between the harmonic series summed only over the primes and the natural logarithm of the natural logarithm:

${\\displaystyle M=\\lim _{n\ ightarrow \\infty }\\left(\\sum _{p\\leq n}{\ rac {1}{p}}-\\ln(\\ln n)\ ight)=\\gamma +\\sum _{p}\\left[\\ln \\!\\left(1-{\ rac {1}{p}}\ ight)+{\ rac {1}{p}}\ ight].}$

Here γ is the Euler–Mascheroni constant, which has an analogous definition involving a sum over all integers (not just the primes).

(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Meissel%E2%80%93Mertens_constant)

Hadamard-de la Vallée-Poussin constant
Kronecker's constant
Mertens constant
prime reciprocal constant

constante de Meissel-Mertens

francés
constante de Hadamard-La Vallée Poussin
constante de Kronecker
constante de Mertens
constante des inverses des nombres premiers

URI

http://data.loterre.fr/ark:/67375/PSR-QTJR2P0K-4

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