DirichletBeta

DirichletBeta[s]
gives the Dirichlet beta function .

DetailsDetails

  • The Dirichlet beta function is also known as the Catalan beta function.
  • DirichletBeta is a mathematical function, suitable for both symbolic and numeric manipulation.
  • For , the Dirichlet beta function is defined as .
  • For certain special arguments, DirichletBeta automatically evaluates to exact values.
  • DirichletBeta is an entire function with branch cut discontinuities.
  • DirichletBeta can be evaluated to arbitrary numerical precision.
  • DirichletBeta automatically threads over lists.

ExamplesExamplesopen allclose all

Basic Examples  (4)Basic Examples  (4)

Plot on the real axis:

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The Dirichlet beta function expands in terms of zeta functions:

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Compute some special values:

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Compute special values of derivatives:

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Introduced in 2014
(10.0)