DirichletBeta

DirichletBeta[s]

gives the Dirichlet beta function .

Details

  • 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.

Examples

Basic Examples  (4)

Plot on the real axis:

The Dirichlet beta function expands in terms of zeta functions:

Compute some special values:

Compute special values of derivatives:

Introduced in 2014
 (10.0)