## Mertens Constant

A constant related to the Twin Primes Constant which appears in the Formula for the sum of inverse Primes

 (1)

which is given by
 (2)

Flajolet and Vardi (1996) show that
 (3)

where is the Euler-Mascheroni Constant, is the Riemann Zeta Function, and is the Möbius Function. The constant also occurs in the Summatory Function of the number of Distinct Prime Factors,
 (4)

(Hardy and Wright 1979, p. 355).

The related constant

 (5)

appears in the Summatory Function of the Divisor Function ,
 (6)

(Hardy and Wright 1979, p. 355).

See also Brun's Constant, Prime Number, Twin Primes Constant

References

Flajolet, P. and Vardi, I. Zeta Function Expansions of Classical Constants.'' Unpublished manuscript. 1996. http://pauillac.inria.fr/algo/flajolet/Publications/landau.ps.

Hardy, G. H. and Weight, E. M. An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Oxford University Press, pp. 351 and 355, 1979.

© 1996-9 Eric W. Weisstein
1999-05-26