Overload List
| # | Signature | Description |
|---|---|---|
| 1 | double FermiDiracCDF(double x, double Mu, double s); | Fermi-Dirac normalization integral (CDF form). |
| 2 | void FermiDiracCDF(TDenseMtxVec *x, double Mu, double s, TDenseMtxVec *y); | Fermi-Dirac cumulative distribution function (CDF). |
Overload 1: double FermiDiracCDF(double x, double Mu, double s);
Fermi-Dirac normalization integral (CDF form).
| # | Name | Type | Description |
|---|---|---|---|
| 1 | x | double | Function domain, real value. NOTE: x is ignored by this routine. |
| 2 | Mu | double | Location (chemical-potential) parameter, real value. |
| 3 | s | double | Shape parameter, real value. |
Returns: the Fermi-Dirac normalization constant. The result is INDEPENDENT of x.
Remarks:
Returns the closed-form normalization integral of the Fermi-Dirac weight over (0,inf), expressed with the Lerch transcendent Phi:
F(mu,s)=e^(mu) Gamma(s+1) Phi(-e^(mu), s+1, 1)
The value does not depend on x. The internal real-valued Lerch series converges for | -e^(mu)| <= 1, i.e. mu <= 0.
Declared in Dew::Math::Units::Probabilities · Dew.Math/Units.Probabilities.h · Cross-compiler
Overload 2: void FermiDiracCDF(TDenseMtxVec *x, double Mu, double s, TDenseMtxVec *y);
Fermi-Dirac cumulative distribution function (CDF).
| # | Name | Type | Description |
|---|---|---|---|
| 1 | x | TDenseMtxVec * | Function domain, real value. |
| 2 | Mu | double | Location parameter, real value. |
| 3 | s | double | Shape parameter, real positive value. |
| 4 | y | TDenseMtxVec * | Contains result. |
Returns: Fermi-Dirac cumulative distribution function (CDF).
Remarks:
The distribution arises in the study of integer spin particles in physics.
Declared in Dew::Math::Units::Probabilities · Dew.Math/Units.Probabilities.h · Cross-compiler