plasma_dispersion_func_deriv

Calculate the derivative of the plasma dispersion function.

Parameters:

zeta (complex, int, float, ndarray, or Quantity) – Argument of plasma dispersion function.

Returns:

Zprime – First derivative of plasma dispersion function.

Return type:

complex, float, or ndarray

Raises:

TypeError – If the argument is invalid.
UnitsError – If the argument is a Quantity but is not dimensionless.
ValueError – If the argument is not entirely finite.

See also

plasma_dispersion_func

Notes

The derivative of the plasma dispersion function is defined as:

\[Z'(\zeta) = \pi^{-1/2} \int_{-\infty}^{+\infty} \frac{e^{-x^2}}{(x-\zeta)^2} dx\]

where the argument is a complex number [Fried and Conte, 1961].

Examples

>>> plasma_dispersion_func_deriv(0)
(-2+0j)
>>> plasma_dispersion_func_deriv(1j)
(-0.484255687717376...+0j)
>>> plasma_dispersion_func_deriv(-1.52+0.47j)
(0.165871331498228...+0.445879788059350...j)

For user convenience plasma_dispersion_func_deriv_lite is bound to this function and can be used as follows:

>>> plasma_dispersion_func_deriv.lite(0)
(-2+0j)
>>> plasma_dispersion_func_deriv.lite(1j)
(-0.484255687717376...+0j)
>>> plasma_dispersion_func_deriv.lite(-1.52+0.47j)
(0.165871331498228...+0.445879788059350...j)