npplus.fermi module¶
Fermi-Dirac integral and inverse of orders -1/2, 1/2, 3/2, 5/2
Notes
See 1 for algorithms.
References
- 1
Antia, H.M., Aph.J Supp. 84, pp. 101-108 (1993).
- fd12(x)[source]¶
Fermi-Dirac integral of order +1/2.
- Parameters
x (array_like) –
- Returns
integral[0 to inf]{ dt * t**0.5 / (exp(t-x)+1) }accurate to about 1e-12.- Return type
ndarray
- fd32(x)[source]¶
Fermi-Dirac integral of order +3/2.
- Parameters
x (array_like) –
- Returns
integral[0 to inf]{ dt * t**1.5 / (exp(t-x)+1) }accurate to about 1e-12.- Return type
ndarray
- fd52(x)[source]¶
Fermi-Dirac integral of order +5/2.
- Parameters
x (array_like) –
- Returns
integral[0 to inf]{ dt * t**2.5 / (exp(t-x)+1) }accurate to about 1e-12.- Return type
ndarray
- fdm12(x)[source]¶
Fermi-Dirac integral of order -1/2.
- Parameters
x (array_like) –
- Returns
integral[0 to inf]{ dt * t**(-0.5) / (exp(t-x)+1) }accurate to about 1e-12.- Return type
ndarray
- ifd12(x)[source]¶
Inverse of Fermi-Dirac integral of order +1/2.
- Parameters
x (array_like) –
- Returns
y – x ==
integral[0 to inf]{ dt * t**0.5 / (exp(t-y)+1) }accurate to about 1e-8.- Return type
ndarray
- ifd32(x)[source]¶
Inverse of Fermi-Dirac integral of order +3/2.
- Parameters
x (array_like) –
- Returns
y – x ==
integral[0 to inf]{ dt * t**1.5 / (exp(t-y)+1) }accurate to about 1e-8.- Return type
ndarray