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Euler Product

For $\sigma>1$,

\begin{displaymath}
\zeta(\sigma)\equiv \sum_{n=1}^\infty {1\over n^\sigma} = \prod_p {1\over 1-{1\over p^\sigma}},
\end{displaymath}

where $\zeta(z)$ is the Riemann Zeta Function.

\begin{displaymath}
e^\gamma=\lim_{n\to\infty} {1\over\ln n} \prod_{i=1}^n {1\over 1-{1\over p_i}},
\end{displaymath}

where the product is over Primes $p$, where $\gamma$ is the Euler-Mascheroni Constant.

See also Dedekind Function




© 1996-9 Eric W. Weisstein
1999-05-25