Dirichlet beta in terms of Lerch transcendent
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Revision as of 00:52, 11 December 2016 by Tom (talk | contribs) (Created page with "==Theorem== The following formula holds: $$\beta(x) = 2^{-x} \Phi \left(-1,x,\dfrac{1}{2} \right),$$ where $\beta$ denotes Dirichlet beta and $\Phi$ denotes the Lerch tr...")
Theorem
The following formula holds: $$\beta(x) = 2^{-x} \Phi \left(-1,x,\dfrac{1}{2} \right),$$ where $\beta$ denotes Dirichlet beta and $\Phi$ denotes the Lerch transcendent.
