docstr: Calculates the real analytical ODF in terms of Spherical
  Harmonics.
docstr_tok: ["Calculates","the","real","analytical","ODF","in","terms","of","Spherical","Harmonics","."]
code: def odf_sh(self):
      r"""Calculates the real analytical ODF in terms of Spherical
      Harmonics.
      """
      # Number of Spherical Harmonics involved in the estimation
      J = (self.radial_order + 1) * (self.radial_order + 2) // 2
  
      # Compute the Spherical Harmonics Coefficients
      c_sh = np.zeros(J)
      counter = 0
  
      for l in range(0, self.radial_order + 1, 2):
          for n in range(l, int((self.radial_order + l) / 2) + 1):
              for m in range(-l, l + 1):
                  j = int(
                      l + m + (2 * np.array(range(0, l, 2)) + 1).sum()
                  )
  
                  Cnl = (
                      ((-1) ** (n - l / 2))
                      / (
                          2.0
                          * (4.0 * np.pi**2 * self.zeta)
                          ** (3.0 / 2.0)
                      )
                      * (
                          (
                              2.0
                              * (4.0 * np.pi**2 * self.zeta)
                              ** (3.0 / 2.0)
                              * factorial(n - l)
                          )
                          / (gamma(n + 3.0 / 2.0))
                      )
                      ** (1.0 / 2.0)
                  )
                  Gnl = (
                      (gamma(l / 2 + 3.0 / 2.0) * gamma(3.0 / 2.0 + n))
                      / (gamma(l + 3.0 / 2.0) * factorial(n - l))
                      * (1.0 / 2.0) ** (-l / 2 - 3.0 / 2.0)
                  )
                  Fnl = hyp2f1(
                      -n + l, l / 2 + 3.0 / 2.0, l + 3.0 / 2.0, 2.0
                  )
  
                  c_sh[j] += self._shore_coef[counter] * Cnl * Gnl * Fnl
                  counter += 1
  
      return c_sh
  
imports: from warnings import warn
  from math import factorial
  import numpy
  from scipy.special import genlaguerre, gamma, hyp2f1
  from dipy.reconst.cache import Cache
  from dipy.reconst.multi_voxel import multi_voxel_fit
  from dipy.reconst.shm import real_sh_descoteaux_from_index
  from dipy.core.geometry import cart2sphere
  from dipy.utils.optpkg import optional_package
label_desc: Use image node_id 4 for calling the ShoreFit obj's underlying member method code with example usage: obj.odf_sh() and returns: c_sh