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- Poussin_proof abstract "In number theory, the Poussin proof is the proof of an identity related to the fractional part of a ratio.In 1838, Peter Gustav Lejeune Dirichlet proved an approximate formula for the average number of divisors of all the numbers from 1 to η:where d represents the divisor function, and γ represents the Euler-Mascheroni constant.In 1898, Charles Jean de la Vallée-Poussin proved that if a large number η is divided by all the primes up to η, then the average fraction by which the quotient falls short of the next whole number is γ:where {x} represents the fractional part of x, and π represents the prime-counting function.For example, if we divide 29 by 2, we get 14.5, which falls short of 15 by 0.5.".
- Poussin_proof wikiPageExternalLink ?IDDOC=268296.
- Poussin_proof wikiPageID "5445552".
- Poussin_proof wikiPageRevisionID "601710599".
- Poussin_proof hasPhotoCollection Poussin_proof.
- Poussin_proof title "Divisor Function".
- Poussin_proof title "Euler-Mascheroni Constant".
- Poussin_proof urlname "DivisorFunction".
- Poussin_proof urlname "Euler-MascheroniConstant".
- Poussin_proof subject Category:Number_theory.
- Poussin_proof comment "In number theory, the Poussin proof is the proof of an identity related to the fractional part of a ratio.In 1838, Peter Gustav Lejeune Dirichlet proved an approximate formula for the average number of divisors of all the numbers from 1 to η:where d represents the divisor function, and γ represents the Euler-Mascheroni constant.In 1898, Charles Jean de la Vallée-Poussin proved that if a large number η is divided by all the primes up to η, then the average fraction by which the quotient falls short of the next whole number is γ:where {x} represents the fractional part of x, and π represents the prime-counting function.For example, if we divide 29 by 2, we get 14.5, which falls short of 15 by 0.5.".
- Poussin_proof label "Poussin proof".
- Poussin_proof sameAs m.0dm73z.
- Poussin_proof sameAs Q7235754.
- Poussin_proof sameAs Q7235754.
- Poussin_proof wasDerivedFrom Poussin_proof?oldid=601710599.
- Poussin_proof isPrimaryTopicOf Poussin_proof.