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 $TemplateBox[{s}, DirichletEta]=sum_(n=0)^infty((-1)^n)/((n+1)^s)$ .
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

open allclose all

Basic Examples (3)

Plot over the reals:

Visualize in the complex plane:

Compute a special value:

Scope (5)

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:

DirichletEta can be used with Interval and CenteredInterval objects:

Properties & Relations (1)

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

Top

Enable JavaScript to interact with content and submit forms on Wolfram websites. Learn how