Feller–Tornier Constant

In mathematics, the Feller–Tornier constant ''C''_FT is the density of the set of all positive integers that have an even number of distinct prime factors raised to a power larger than one (ignoring any prime factors which appear only to the first power).
It is named after William Feller (1906–1970) and Erhard Tornier (1894–1982)

:
\begin
C_\text & =+\left( \prod_^\infty \left(1- \right) \right) \\ pt& = \left(1+ \prod_^\infty \left(1 - \right) \right) \\ pt& = \left(1+ \prod_^\infty \left( 1- \right) \right) \\ pt& = + \prod_^\infty \left( 1- \right)= 0.66131704946\ldots
\end

Omega function

The Big Omega function is given by

: $\Omega(x) = \text x \text$

See also: Prime omega function.

The Iverson bracket is

: = \begin 1 & \text P \text \\ 0 & \text P \text \end

With these notations, we have

: $C_\text= \lim_ \frac$

Prime zeta function

The prime zeta function ''P'' is give by

: $P(s) = \sum_ \frac 1 .$

The Feller–Tornier constant satisfies

: $C_\text= \left( 1+ \exp \left( -\sum_^\infty \right) \right).$

See also

*Riemann zeta function
*L-function
*Euler product
*Twin prime

References

{{DEFAULTSORT:Feller-Tornier constant
Mathematical constants
Zeta and L-functions
Infinite products