Difference between revisions of "Dirichlet beta"
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Revision as of 08:11, 19 January 2015
The Dirichlet $\beta$ function is defined by $$\beta(x) = \displaystyle\sum_{k=0}^{\infty} (-1)^k (2k+1)^{-x} = 2^{-x} \Phi \left(-1,x,\dfrac{1}{2} \right),$$ where $\Phi$ denotes the Lerch transcendent.
