\begin{definition}[Definition:Landau-Ramanujan Constant]
The '''Landau-Ramanujan constant''' is the real number $k$ defined as:
{{begin-eqn}}
{{eqn | l = k
      | r = \sqrt {\dfrac 1 2 \ds \prod_{\substack {r \mathop = 4 n \mathop + 3 \\ \text {$r$ prime} } } \paren {1 - \dfrac 1 {r^2} }^{-1} }
}}
{{eqn | o = \approx
      | r = 0 \cdotp 76422 \, 3653 \ldots
}}
{{end-eqn}}
{{OEIS|A064533}}
\end{definition}