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: Raises: TypeError
– If the argument is invalid.UnitsError
– If the argument is aQuantity
but is not dimensionless.ValueError
– If the argument is not entirely finite.
See also
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)