plasma_dispersion_func_deriv

plasmapy.dispersion.dispersion_functions.plasma_dispersion_func_deriv(

zeta: complex | ndarray | Annotated[Quantity, Unit(dimensionless)],

) → complex | ndarray | Annotated[Quantity, Unit(dimensionless)]

Calculate the derivative of the plasma dispersion function.

The derivative of the plasma dispersion function is:

\[Z'(ζ) = π^{-1/2} \int_{-∞}^{+∞} \frac{e^{-x^2}}{(x-ζ)^2} dx\]

where the argument \(ζ\) is a complex number [Fried and Conte, 1961].

Parameters:

zeta (array_like or Quantity) – Argument of plasma dispersion function.

Returns:

First derivative of plasma dispersion function.

Return type:

complex, ndarray, or Quantity

Raises:

UnitsError – If the argument is a Quantity but is not dimensionless.

See also

None

Examples

>>> plasma_dispersion_func_deriv(0)
np.complex128(-2+0j)
>>> plasma_dispersion_func_deriv(1j)
np.complex128(-0.48425568771737604+0j)
>>> plasma_dispersion_func_deriv(-1.52 + 0.47j)
np.complex128(0.165871331...+0.4458797880...j)