Difference between revisions of "Dirichlet beta"
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The Dirichlet $\beta$ function is defined by | The Dirichlet $\beta$ function is defined by | ||
| − | $$\beta( | + | $$\beta(z) = \displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^k}{(2k+1)^z}.$$ |
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=Properties= | =Properties= | ||
| − | + | [[Catalan's constant using Dirichlet beta]]<br /> | |
| + | [[Dirichlet beta in terms of Lerch transcendent]]<br /> | ||
[[Category:SpecialFunction]] | [[Category:SpecialFunction]] | ||
Latest revision as of 00:54, 11 December 2016
The Dirichlet $\beta$ function is defined by $$\beta(z) = \displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^k}{(2k+1)^z}.$$
Graph of $\beta$ on $[-4,4]$.
Domain coloring of analytic continuation of $\beta$.
Properties
Catalan's constant using Dirichlet beta
Dirichlet beta in terms of Lerch transcendent
