Definition:Dirichlet Beta Function

Definition

The Dirichlet beta function $\beta$ is the complex function defined on the half-plane $\map \Re s > 0$ by the series:

$\ds \map \beta s = \sum_{n \mathop = 0}^\infty \frac {\paren {-1}^n} {\paren {2 n + 1}^s}$

Also see

• Results about the Dirichlet $\beta$ function can be found here.

Source of Name

This entry was named for Johann Peter Gustav Lejeune Dirichlet.

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Dirichlet beta function

• Weisstein, Eric W. "Digamma Function." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DigammaFunction.html