# scipy.special.voigt_profile

scipy.special.voigt_profile(x, sigma, gamma, out=None) = <ufunc 'voigt_profile'>

  Voigt profile.

  The Voigt profile is a convolution of a 1-D Normal distribution with standard deviation `sigma` and a 1-D Cauchy distribution with half-width at half-maximum `gamma`.

  If `sigma = 0`, PDF of Cauchy distribution is returned. Conversely, if `gamma = 0`, PDF of Normal distribution is returned. If `sigma = gamma = 0`, the return value is `Inf` for `x = 0`, and `0` for all other `x`.

  Parameters
    x array_like

      Real argument

    sigma array_like

      The standard deviation of the Normal distribution part

    gamma array_like

      The half-width at half-maximum of the Cauchy distribution part

    out ndarray, optional

      Optional output array for the function values

  Returns
    scalar or ndarray

      The Voigt profile at the given arguments

  See also

  `wofz`

    Faddeeva function

  Notes

  It can be expressed in terms of Faddeeva function

  \[V(x; \sigma, \gamma) = \frac{Re[w(z)]}{\sigma\sqrt{2\pi}},\]
  \[z = \frac{x + i\gamma}{\sqrt{2}\sigma}\]

  where \(w(z)\) is the Faddeeva function.

  References

  1

    https://en.wikipedia.org/wiki/Voigt_profile

scipy.special.modfresnelm scipy.special.erf_zeros