Category:Catalan's Constant
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This category contains results about Catalan's Constant.
Catalan's constant is the real number defined as:
| \(\ds G\) | \(=\) | \(\ds \map \beta 2\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \sum_{n \mathop = 0}^{\infty} \frac{\paren {-1}^n} {\paren {2 n + 1}^2}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \frac 1 {1^2} - \frac 1 {3^2} + \frac 1 {5^2} - \frac 1 {7^2} + \cdots\) |
where $\beta$ is the Dirichlet beta function.
Its numerical value is approximately:
- $G = 0 \cdotp 91596 \, 55941 \, 77219 \, 01505 \, 46035 \, 14932 \, 38411 \, 0774 \ldots$
Pages in category "Catalan's Constant"
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