\begin{definition}[Definition:Catalan's Constant]
'''Catalan's constant''' is the real number defined as:
{{begin-eqn}}
{{eqn | l = G
      | r = \map \beta 2
      | c = 
}}
{{eqn | r = \sum_{n \mathop = 0}^{\infty} \frac{\paren {-1}^n} {\paren {2 n + 1}^2}
      | c = 
}}
{{eqn | r = \frac 1 {1^2} - \frac 1 {3^2} + \frac 1 {5^2} - \frac 1 {7^2} + \cdots
      | c = 
}}
{{end-eqn}}
where $\beta$ is the Dirichlet beta function.
Its numerical value is approximately:
:$G = 0 \cdotp 91596 \, 55941 \, 77219 \, 01505 \, 46035 \, 14932 \, 38411 \, 0774 \ldots$
{{OEIS|A006752}}
{{NamedforDef|Eugène Charles Catalan|cat = Catalan}}
\end{definition}