plasma_dispersion_func_deriv

plasmapy.dispersion.dispersionfunction.plasma_dispersion_func_deriv(zeta: Union[complex, int, float, numpy.ndarray, astropy.units.quantity.Quantity]) → Union[complex, float, numpy.ndarray, astropy.units.quantity.Quantity]

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 [1].

References

[1]	Fried, Burton D. and Samuel D. Conte. 1961. The Plasma Dispersion Function: The Hilbert Transformation of the Gaussian. Academic Press (New York and London). ISBN 9781483261737

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)