Difference between revisions of "Catalan's constant"

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Catalan's constant is
 
Catalan's constant is
$$G=\displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^k}{(2k+1)^2} = 0.915 965 594 177 219 015 054 603 514 932 384 110 774 \ldots.$$
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$$K=\displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^k}{(2k+1)^2} = 0.915 965 594 177 219 015 054 603 514 932 384 110 774 \ldots.$$
 
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]].
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=Properties=
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[[Catalan's constant using Dirichlet beta]]<br />
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[[Catalan's constant using Legendre chi]]<br />
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[[Catalan's constant using Hurwitz zeta]]<br />
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[[Category:SpecialFunction]]

Latest revision as of 15:40, 25 February 2018

Catalan's constant is $$K=\displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^k}{(2k+1)^2} = 0.915 965 594 177 219 015 054 603 514 932 384 110 774 \ldots.$$ This means that Catalan's constant can be expressed as $\beta(2)$ where $\beta$ is the Dirichlet beta function.

Properties

Catalan's constant using Dirichlet beta
Catalan's constant using Legendre chi
Catalan's constant using Hurwitz zeta