function DirichletLambda(const Z: TCplx; n: Integer): TCplx;
Dirichlet Lambda function.
| # | Name | Description |
|---|---|---|
| 1 | Z | complex value at which the Lambda function is evaluated. |
| 2 | n | number of terms used in the complex series approximation (default 64). |
Returns: TCplx (complex) - 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.