Probabilities.BoseEinsteinCDF Method

function BoseEinsteinCDF(x: Double; Mu: Double; s: Double): Double;

Bose-Einstein normalization integral (CDF form).

#NameDescription
1xFunction domain, real value. NOTE: x is ignored by this routine.
2MuLocation (chemical-potential) parameter, real value.
3sShape parameter, real value.

Returns: Double - the Bose-Einstein normalization constant. The result is INDEPENDENT of x.

Remarks:

Returns the closed-form normalization integral of the Bose-Einstein 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 parameter is accepted only for signature symmetry). The internal real-valued Lerch series converges for e^(mu) <= 1, i.e. mu <= 0.

See Also: Probabilities.BoseEinsteinPDF, Probabilities.FermiDiracCDF