TCplx DirichletEta(const TCplx &Z, int n = 64);
Dirichlet Eta function.
| # | Name | Type | Description |
|---|---|---|---|
| 1 | Z | const TCplx & | complex value at which the Eta function is evaluated. |
| 2 | n = 64 | int | number of terms used in the complex series approximation (default 64). |
Returns: the Dirichlet Eta function evaluated at the complex point Z.
Remarks:
The Dirichlet eta function (alternating zeta function) is defined by
eta(z) = sum_(n=1)^(inf)((-1)^(n-1))/n^z = (1-2^(1-z))zeta(z) .
Domain: any complex Z. Defined behavior: it is evaluated with an Euler / van Wijngaarden acceleration of the alternating series, using the reflection point z |-> 1-z for Re(z) < 1/2; special-cased exactly to 1/2 at z=0 and to ln 2 at z=1 (removable point). On the real axis the imaginary part of the result is zero. Known value: eta(2)=pi^2/12.
Declared in Dew::Math::Units::Probabilities · Dew.Math/Units.Probabilities.h · Cross-compiler