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Mertens, Second Theorem

المؤلف:  Havil, J

المصدر:  Gamma: Exploring Euler,s Constant. Princeton, NJ: Princeton University Press

الجزء والصفحة:  ...

19-3-2020

1046

Mertens' Second Theorem

Mertens' second theorem states that the asymptotic form of the harmonic series for the sum of reciprocal primes is given by

where  is a prime,  is a constant known as the Mertens constant, and  is a Landau symbol.

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REFERENCES:

Havil, J. Gamma: Exploring Euler's Constant. Princeton, NJ: Princeton University Press, p. 109, 2003.

Tenenbaum, G. and Mendes-France, M. The Prime Numbers and Their Distribution. Providence, RI: Amer. Math. Soc., p. 22, 2000.