Probabilities::FermiDiracCDF Function

Overload List

#SignatureDescription
1double FermiDiracCDF(double x, double Mu, double s);Fermi-Dirac normalization integral (CDF form).
2void 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).

#NameTypeDescription
1xdoubleFunction domain, real value. NOTE: x is ignored by this routine.
2MudoubleLocation (chemical-potential) parameter, real value.
3sdoubleShape 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.

See Also: Probabilities::BoseEinsteinCDF, Probabilities::FermiDiracPDF
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).

#NameTypeDescription
1xTDenseMtxVec *Function domain, real value.
2MudoubleLocation parameter, real value.
3sdoubleShape parameter, real positive value.
4yTDenseMtxVec *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