# scipy.special.ellip_normal

scipy.special.ellip_normal(h2, k2, n, p)

  Ellipsoidal harmonic normalization constants gamma^p_n

  The normalization constant is defined as

  \[\gamma^p_n=8\int_{0}^{h}dx\int_{h}^{k}dy\frac{(y^2-x^2)(E^p_n(y)E^p_n(x))^2}{\sqrt((k^2-y^2)(y^2-h^2)(h^2-x^2)(k^2-x^2)}\]
  Parameters:
    h2 float

      `h**2`

    k2 float

      `k**2`; should be larger than `h**2`

    n int

      Degree.

    p int

      Order, can range between [1,2n+1].

  Returns:
    gamma float

      The normalization constant \(\gamma^p_n\)

  See also

  `ellip_harm`, `ellip_harm_2`

  Notes

  New in version 0.15.0.

  Examples

      >>> from scipy.special import ellip_normal
      >>> w = ellip_normal(5,8,3,7)
      >>> w
      1723.38796997