Difference between revisions of "Meissel-Mertens constant"
From specialfunctionswiki
| (One intermediate revision by the same user not shown) | |||
| Line 4: | Line 4: | ||
=Properties= | =Properties= | ||
| − | + | [[Meissel-Mertens constant in terms of the Euler-Mascheroni constant]] | |
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
=See Also= | =See Also= | ||
[[Euler-Mascheroni constant]] | [[Euler-Mascheroni constant]] | ||
| + | |||
| + | [[Category:SpecialFunction]] | ||
Latest revision as of 00:28, 20 August 2016
The Meissel-Mertens constant (also known as Mertens' constant, Kronecker's constant, the Hadamard-de la Vallée-Poussin constant, or prime reciprocal constant) is $$M=\displaystyle\lim_{n \rightarrow \infty} \left( \displaystyle\sum_{p \leq n;p \mathrm{\hspace{2pt} prime}} \dfrac{1}{p} - \log(\log(n)) \right).$$ Note that the sum $\displaystyle\sum_{p \leq n;p \mathrm{\hspace{2pt} prime}} \dfrac{1}{p}$ diverges, so this definition resembles that of the Euler-Mascheroni constant.
Properties
Meissel-Mertens constant in terms of the Euler-Mascheroni constant
