Module rgsl::fermi_dirac::complete_integrals
[−]
[src]
The complete Fermi-Dirac integral F_j(x) is given by,
F_j(x) := (1/\Gamma(j+1)) \int_0\infty dt (tj / (\exp(t-x) + 1))
Note that the Fermi-Dirac integral is sometimes defined without the normalisation factor in other texts.
Functions
| fermi_dirac_0 |
This routine computes the complete Fermi-Dirac integral with an index of 0. This integral is given by F_0(x) = \ln(1 + ex). |
| fermi_dirac_1 |
This routine computes the complete Fermi-Dirac integral with an index of 1, F_1(x) = \int_0\infty dt (t /(\exp(t-x)+1)). |
| fermi_dirac_2 |
This routine computes the complete Fermi-Dirac integral with an index of 2, F_2(x) = (1/2) \int_0\infty dt (t2 /(\exp(t-x)+1)). |
| fermi_dirac_0_e |
This routine computes the complete Fermi-Dirac integral with an index of 0. This integral is given by F_0(x) = \ln(1 + ex). |
| fermi_dirac_1_e |
This routine computes the complete Fermi-Dirac integral with an index of 1, F_1(x) = \int_0\infty dt (t /(\exp(t-x)+1)). |
| fermi_dirac_2_e |
This routine computes the complete Fermi-Dirac integral with an index of 2, F_2(x) = (1/2) \int_0\infty dt (t2 /(\exp(t-x)+1)). |
| fermi_dirac_3half |
This routine computes the complete Fermi-Dirac integral F_{3/2}(x). |
| fermi_dirac_3half_e |
This routine computes the complete Fermi-Dirac integral F_{3/2}(x). |
| fermi_dirac_half |
This routine computes the complete Fermi-Dirac integral F_{1/2}(x). |
| fermi_dirac_half_e |
This routine computes the complete Fermi-Dirac integral F_{1/2}(x). |
| fermi_dirac_int |
This routine computes the complete Fermi-Dirac integral with an integer index of j, F_j(x) = (1/\Gamma(j+1)) \int_0\infty dt (tj /(\exp(t-x)+1)). |
| fermi_dirac_int_e |
This routine computes the complete Fermi-Dirac integral with an integer index of j, F_j(x) = (1/\Gamma(j+1)) \int_0\infty dt (tj /(\exp(t-x)+1)). |
| fermi_dirac_m1 |
This routine computes the complete Fermi-Dirac integral with an index of -1. This integral is given by F_{-1}(x) = ex / (1 + ex). |
| fermi_dirac_m1_e |
This routine computes the complete Fermi-Dirac integral with an index of -1. This integral is given by F_{-1}(x) = ex / (1 + ex). |
| fermi_dirac_mhalf |
This routine computes the complete Fermi-Dirac integral F_{-1/2}(x). |
| fermi_dirac_mhalf_e |
This routine computes the complete Fermi-Dirac integral F_{-1/2}(x). |