# DirichletEta

DirichletEta[s]

gives the Dirichlet eta function .

# Details

• The Dirichlet eta function is also known as the alternating zeta function.
• DirichletEta is a mathematical function, suitable for both symbolic and numeric manipulation.
• For , the Dirichlet eta function is defined as .
• For certain special arguments, DirichletEta automatically evaluates to exact values.
• DirichletEta is an entire function with branch cut discontinuities.
• DirichletEta can be evaluated to arbitrary numerical precision.
• DirichletEta automatically threads over lists.
• DirichletEta can be used with Interval and CenteredInterval objects. »

# Examples

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## Basic Examples(3)

Plot over the reals:

Visualize in the complex plane:

Compute a special value:

## Scope(6)

DirichletEta is neither non-decreasing nor non-increasing:

DirichletEta is not injective:

DirichletEta is neither non-negative nor non-positive:

DirichletEta is neither convex nor concave:

Compute worst-case guaranteed intervals using Interval and CenteredInterval objects:

Or compute average-case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix DirichletEta function using MatrixFunction:

## Properties & Relations(1)

Verify the interrelationship among the DirichletEta, DirichletLambda and Zeta functions:

Wolfram Research (2014), DirichletEta, Wolfram Language function, https://reference.wolfram.com/language/ref/DirichletEta.html (updated 2022).

#### Text

Wolfram Research (2014), DirichletEta, Wolfram Language function, https://reference.wolfram.com/language/ref/DirichletEta.html (updated 2022).

#### CMS

Wolfram Language. 2014. "DirichletEta." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/DirichletEta.html.

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_dirichleteta, author="Wolfram Research", title="{DirichletEta}", year="2022", howpublished="\url{https://reference.wolfram.com/language/ref/DirichletEta.html}", note=[Accessed: 12-August-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_dirichleteta, organization={Wolfram Research}, title={DirichletEta}, year={2022}, url={https://reference.wolfram.com/language/ref/DirichletEta.html}, note=[Accessed: 12-August-2024 ]}