Complete Fermi-Dirac Integrals
The complete Fermi-Dirac integral F_j(x) is given by,
F_j(x) := (1/r\Gamma(j+1)) \int_0^\infty (t^j / (\exp(t-x) + 1))
- Function: double gsl_sf_fermi_dirac_m1 (double x)
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- Function: int gsl_sf_fermi_dirac_m1_e (double x, gsl_sf_result * result)
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These routines compute the complete Fermi-Dirac integral with an index of -1.
This integral is given by
F_{-1}(x) = e^x / (1 + e^x).
- Function: double gsl_sf_fermi_dirac_0 (double x)
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- Function: int gsl_sf_fermi_dirac_0_e (double x, gsl_sf_result * result)
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These routines compute the complete Fermi-Dirac integral with an index of 0.
This integral is given by F_0(x) = \ln(1 + e^x).
- Function: double gsl_sf_fermi_dirac_1 (double x)
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- Function: int gsl_sf_fermi_dirac_1_e (double x, gsl_sf_result * result)
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These routines compute the complete Fermi-Dirac integral with an index of 1,
F_1(x) = \int_0^\infty dt (t /(\exp(t-x)+1)).
- Function: double gsl_sf_fermi_dirac_2 (double x)
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- Function: int gsl_sf_fermi_dirac_2_e (double x, gsl_sf_result * result)
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These routines compute the complete Fermi-Dirac integral with an index
of 2,
F_2(x) = (1/2) \int_0^\infty dt (t^2 /(\exp(t-x)+1)).
- Function: double gsl_sf_fermi_dirac_int (int j, double x)
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- Function: int gsl_sf_fermi_dirac_int_e (int j, double x, gsl_sf_result * result)
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These routines compute the complete Fermi-Dirac integral with an integer
index of j,
F_j(x) = (1/\Gamma(j+1)) \int_0^\infty dt (t^j /(\exp(t-x)+1)).
- Function: double gsl_sf_fermi_dirac_mhalf (double x)
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- Function: int gsl_sf_fermi_dirac_mhalf_e (double x, gsl_sf_result * result)
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These routines compute the complete Fermi-Dirac integral
F_{-1/2}(x).
- Function: double gsl_sf_fermi_dirac_half (double x)
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- Function: int gsl_sf_fermi_dirac_half_e (double x, gsl_sf_result * result)
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These routines compute the complete Fermi-Dirac integral
F_{1/2}(x).
- Function: double gsl_sf_fermi_dirac_3half (double x)
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- Function: int gsl_sf_fermi_dirac_3half_e (double x, gsl_sf_result * result)
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These routines compute the complete Fermi-Dirac integral
F_{3/2}(x).