Concept information
Preferred term
Meissel-Mertens constant
Definition(s)
-
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:
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)
![{\\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].}](https://wikimedia.org/api/rest_v1/media/math/render/svg/c0284c04584369156c34bad21ea0010f128f8696)
Broader concept(s)
Synonym(s)
- Hadamard-de la Vallée-Poussin constant
- Kronecker's constant
- Mertens constant
- prime reciprocal constant
In other languages
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French
-
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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