Definition:Dirichlet Beta Function
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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