TCplx DirichletLambda(const TCplx &Z, int n = 64);
Dirichlet Lambda function.
| # | Name | Type | Description |
|---|---|---|---|
| 1 | Z | const TCplx & | complex value at which the Lambda function is evaluated. |
| 2 | n = 64 | int | number of terms used in the complex series approximation (default 64). |
Returns: the Dirichlet Lambda function evaluated at the complex point Z.
Remarks:
The Dirichlet lambda function is defined by
lambda(z) = sum_(n=0)^(inf)1/((2n+1)^z) = (1-2^(-z))zeta(z) ,
and is related to the Riemann zeta and Dirichlet eta functions by zeta(z)/2^z=lambda(z)/(2^z-1)=eta(z)/(2^z-2).
Domain: any complex Z with 2^z != 2. Defined behavior: it is computed as lambda(z)=eta(z) (2^z-1)/(2^z-2) from Probabilities::DirichletEta; at z=1 (where 2^z=2) the result is complex infinity. On the real axis the imaginary part of the result is zero. Known value: lambda(2)=pi^2/8.
Declared in Dew::Math::Units::Probabilities · Dew.Math/Units.Probabilities.h · Cross-compiler