Difference between revisions of "Catalan's constant"
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| − | + | Catalan's constant is | |
$$G=\displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^k}{(2k+1)^2} = 0.915 965 594 177 219 015 054 603 514 932 384 110 774 \ldots.$$ | $$G=\displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^k}{(2k+1)^2} = 0.915 965 594 177 219 015 054 603 514 932 384 110 774 \ldots.$$ | ||
This means that Catalan's constant can be expressed as $\beta(2)$ where $\beta$ is the [[Dirichlet beta function]]. | This means that Catalan's constant can be expressed as $\beta(2)$ where $\beta$ is the [[Dirichlet beta function]]. | ||
Revision as of 01:11, 21 March 2015
Catalan's constant is $$G=\displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^k}{(2k+1)^2} = 0.915 965 594 177 219 015 054 603 514 932 384 110 774 \ldots.$$ This means that Catalan's constant can be expressed as $\beta(2)$ where $\beta$ is the Dirichlet beta function.
