# DirichletLambda

gives the Dirichlet lambda function .

# Details

• Mathematical function, suitable for both symbolic and numeric manipulation.
• For , the Dirichlet lambda function is defined as .
• For certain special arguments, DirichletLambda automatically evaluates to exact values.
• DirichletLambda has no branch cut discontinuities.
• DirichletLambda can be evaluated to arbitrary numerical precision.
• DirichletLambda automatically threads over lists.

# Examples

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## Basic Examples(4)

Plot on the real axis:

Visualize in the complex plane:

The Dirichlet lambda function expands in terms of zeta functions:

Compute some special values:

## Scope(8)

DirichletLambda is not an analytic function:

DirichletLambda has both singularity and discontinuity at x=1:

DirichletLambda is meromorphic:

It has a simple pole at :

DirichletLambda is neither non-decreasing nor non-increasing:

DirichletLambda is not injective:

DirichletLambda is neither non-negative nor non-positive:

DirichletLambda is neither convex nor concave:

Compute average-case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix DirichletLambda function using MatrixFunction:

## Properties & Relations(1)

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

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

#### Text

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

#### CMS

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

#### APA

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

#### BibTeX

@misc{reference.wolfram_2024_dirichletlambda, author="Wolfram Research", title="{DirichletLambda}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/DirichletLambda.html}", note=[Accessed: 13-August-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_dirichletlambda, organization={Wolfram Research}, title={DirichletLambda}, year={2014}, url={https://reference.wolfram.com/language/ref/DirichletLambda.html}, note=[Accessed: 13-August-2024 ]}