parameters: (h2, k2, n, p, s, signm=1, signn=1)
return_statement: return _ellip_harm(h2, k2, n, p, s, signm, signn)
docstring: r"""
      Ellipsoidal harmonic functions E^p_n(l)
  
      These are also known as Lame functions of the first kind, and are
      solutions to the Lame equation:
  
      .. math:: (s^2 - h^2)(s^2 - k^2)E''(s) + s(2s^2 - h^2 - k^2)E'(s) + (a - q s^2)E(s) = 0
  
      where :math:`q = (n+1)n` and :math:`a` is the eigenvalue (not
      returned) corresponding to the solutions.
  
      Parameters
      ----------
      h2 : float
          ``h**2``
      k2 : float
          ``k**2``; should be larger than ``h**2``
      n : int
          Degree
      s : float
          Coordinate
      p : int
          Order, can range between [1,2n+1]
      signm : {1, -1}, optional
          Sign of prefactor of functions. Can be +/-1. See Notes.
      signn : {1, -1}, optional
          Sign of prefactor of functions. Can be +/-1. See Notes.
  
      Returns
      -------
      E : float
          the harmonic :math:`E^p_n(s)`
  
      See Also
      --------
      ellip_harm_2, ellip_normal
  
      Notes
      -----
      The geometric interpretation of the ellipsoidal functions is
      explained in [2]_, [3]_, [4]_.  The `signm` and `signn` arguments control the
      sign of prefactors for functions according to their type::
  
          K : +1
          L : signm
          M : signn
          N : signm*signn
  
      .. versionadded:: 0.15.0
  
      References
      ----------
      .. [1] Digital Library of Mathematical Functions 29.12
         https://dlmf.nist.gov/29.12
      .. [2] Bardhan and Knepley, "Computational science and
         re-discovery: open-source implementations of
         ellipsoidal harmonics for problems in potential theory",
         Comput. Sci. Disc. 5, 014006 (2012)
         :doi:`10.1088/1749-4699/5/1/014006`.
      .. [3] David J.and Dechambre P, "Computation of Ellipsoidal
         Gravity Field Harmonics for small solar system bodies"
         pp. 30-36, 2000
      .. [4] George Dassios, "Ellipsoidal Harmonics: Theory and Applications"
         pp. 418, 2012
  
      Examples
      --------
      >>> from scipy.special import ellip_harm
      >>> w = ellip_harm(5,8,1,1,2.5)
      >>> w
      2.5
  
      Check that the functions indeed are solutions to the Lame equation:
  
      >>> from scipy.interpolate import UnivariateSpline
      >>> def eigenvalue(f, df, ddf):
      ...     r = ((s**2 - h**2)*(s**2 - k**2)*ddf + s*(2*s**2 - h**2 - k**2)*df - n*(n+1)*s**2*f)/f
      ...     return -r.mean(), r.std()
      >>> s = np.linspace(0.1, 10, 200)
      >>> k, h, n, p = 8.0, 2.2, 3, 2
      >>> E = ellip_harm(h**2, k**2, n, p, s)
      >>> E_spl = UnivariateSpline(s, E)
      >>> a, a_err = eigenvalue(E_spl(s), E_spl(s,1), E_spl(s,2))
      >>> a, a_err
      (583.44366156701483, 6.4580890640310646e-11)
docstring_summary: r"""
      Ellipsoidal harmonic functions E^p_n(l)
docstring_tokens: r Ellipsoidal harmonic functions E^p_n ( l )
function: def ellip_harm(h2, k2, n, p, s, signm=1, signn=1):
      r"""
      Ellipsoidal harmonic functions E^p_n(l)
  
      These are also known as Lame functions of the first kind, and are
      solutions to the Lame equation:
  
      .. math:: (s^2 - h^2)(s^2 - k^2)E''(s) + s(2s^2 - h^2 - k^2)E'(s) + (a - q s^2)E(s) = 0
  
      where :math:`q = (n+1)n` and :math:`a` is the eigenvalue (not
      returned) corresponding to the solutions.
  
      Parameters
      ----------
      h2 : float
          ``h**2``
      k2 : float
          ``k**2``; should be larger than ``h**2``
      n : int
          Degree
      s : float
          Coordinate
      p : int
          Order, can range between [1,2n+1]
      signm : {1, -1}, optional
          Sign of prefactor of functions. Can be +/-1. See Notes.
      signn : {1, -1}, optional
          Sign of prefactor of functions. Can be +/-1. See Notes.
  
      Returns
      -------
      E : float
          the harmonic :math:`E^p_n(s)`
  
      See Also
      --------
      ellip_harm_2, ellip_normal
  
      Notes
      -----
      The geometric interpretation of the ellipsoidal functions is
      explained in [2]_, [3]_, [4]_.  The `signm` and `signn` arguments control the
      sign of prefactors for functions according to their type::
  
          K : +1
          L : signm
          M : signn
          N : signm*signn
  
      .. versionadded:: 0.15.0
  
      References
      ----------
      .. [1] Digital Library of Mathematical Functions 29.12
         https://dlmf.nist.gov/29.12
      .. [2] Bardhan and Knepley, "Computational science and
         re-discovery: open-source implementations of
         ellipsoidal harmonics for problems in potential theory",
         Comput. Sci. Disc. 5, 014006 (2012)
         :doi:`10.1088/1749-4699/5/1/014006`.
      .. [3] David J.and Dechambre P, "Computation of Ellipsoidal
         Gravity Field Harmonics for small solar system bodies"
         pp. 30-36, 2000
      .. [4] George Dassios, "Ellipsoidal Harmonics: Theory and Applications"
         pp. 418, 2012
  
      Examples
      --------
      >>> from scipy.special import ellip_harm
      >>> w = ellip_harm(5,8,1,1,2.5)
      >>> w
      2.5
  
      Check that the functions indeed are solutions to the Lame equation:
  
      >>> from scipy.interpolate import UnivariateSpline
      >>> def eigenvalue(f, df, ddf):
      ...     r = ((s**2 - h**2)*(s**2 - k**2)*ddf + s*(2*s**2 - h**2 - k**2)*df - n*(n+1)*s**2*f)/f
      ...     return -r.mean(), r.std()
      >>> s = np.linspace(0.1, 10, 200)
      >>> k, h, n, p = 8.0, 2.2, 3, 2
      >>> E = ellip_harm(h**2, k**2, n, p, s)
      >>> E_spl = UnivariateSpline(s, E)
      >>> a, a_err = eigenvalue(E_spl(s), E_spl(s,1), E_spl(s,2))
      >>> a, a_err
      (583.44366156701483, 6.4580890640310646e-11)
  
      """
      return _ellip_harm(h2, k2, n, p, s, signm, signn)
function_tokens: def ellip_harm ( h2 , k2 , n , p , s , signm = 1 , signn = 1 ) : return _ellip_harm ( h2 , k2 , n , p , s , signm , signn )