# DirichletBeta

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

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## Basic Examples(4)

Plot on the real axis:

Visualize in the complex plane:

The Dirichlet beta function expands in terms of zeta functions:

Compute some special values:

## Scope(7)

DirichletBeta is neither non-decreasing nor non-increasing:

DirichletBeta is not injective:

DirichletBeta is neither non-negative nor non-positive:

DirichletBeta is neither convex nor concave:

Compute special values of derivatives:

Compute average-case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix DirichletBeta function using MatrixFunction:

Wolfram Research (2014), DirichletBeta, Wolfram Language function, https://reference.wolfram.com/language/ref/DirichletBeta.html.

#### Text

Wolfram Research (2014), DirichletBeta, Wolfram Language function, https://reference.wolfram.com/language/ref/DirichletBeta.html.

#### CMS

Wolfram Language. 2014. "DirichletBeta." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/DirichletBeta.html.

#### APA

Wolfram Language. (2014). DirichletBeta. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DirichletBeta.html

#### BibTeX

@misc{reference.wolfram_2024_dirichletbeta, author="Wolfram Research", title="{DirichletBeta}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/DirichletBeta.html}", note=[Accessed: 02-August-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_dirichletbeta, organization={Wolfram Research}, title={DirichletBeta}, year={2014}, url={https://reference.wolfram.com/language/ref/DirichletBeta.html}, note=[Accessed: 02-August-2024 ]}