Difference between revisions of "Catalan's constant"
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(Created page with "The Catalan constant is $$G=\displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^k}{(2k+1)^2}.$$ This means that Catalan's constant can be expressed as $\beta(2)$ where $\beta$ is the...") |
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| − | + | 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.$$ |
This means that Catalan's constant can be expressed as $\beta(2)$ where $\beta$ is the [[Dirichlet beta function]]. | This means that Catalan's constant can be expressed as $\beta(2)$ where $\beta$ is the [[Dirichlet beta function]]. | ||
| + | |||
| + | =Properties= | ||
| + | [[Catalan's constant using Dirichlet beta]]<br /> | ||
| + | [[Catalan's constant using Legendre chi]]<br /> | ||
| + | [[Catalan's constant using Hurwitz zeta]]<br /> | ||
| + | |||
| + | [[Category:SpecialFunction]] | ||
Latest revision as of 15:40, 25 February 2018
Catalan's constant is $$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
