Dirichlet Beta Function - Functional Equation

Functional Equation

The functional equation extends the beta function to the left side of the complex plane Re(s)<0. It is given by

$\beta(s)=\left(\frac{\pi}{2}\right)^{s-1} \Gamma(1-s) \cos \frac{\pi s}{2}\,\beta(1-s)$

where Γ(s) is the gamma function.

Read more about this topic: Dirichlet Beta Function

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