Computes the Dirichlet eta function.

Namespace: Meta.Numerics.Functions
Assembly: Meta.Numerics (in Meta.Numerics.dll) Version: 2.1.0.0 (2.1.0.0)

Syntax

            
 C#  Visual Basic  Visual C++  F# 
public static double DirichletEta(
	double s
)
Public Shared Function DirichletEta ( _
	s As Double _
) As Double
public:
static double DirichletEta(
	double s
)
static member DirichletEta : 
        s : float -> float

Parameters

s
Double
The argument, which must be non-negative.

Return Value

The value of η(s).

Remarks

The Dirichlet eta function is the sum of the sth inverse power of the natural numbers, with alternating signs.

Because these are just the terms of the Riemann zeta function (RiemannZeta(Double)) with alternating signs, it is also called the alternating zeta function.

It can be related to the Riemann ζ function.

Exceptions

ExceptionCondition
System..::..ArgumentOutOfRangeExceptions is negative.

See Also