code: def carlson_rf(x, y, z, errtol=3e-4):
      r"""Compute the Carlson's incomplete elliptic integral of the first kind
  
      Carlson's incomplete elliptic integral of the first kind is defined as:
  
      .. math::
  
          R_F = \frac{1}{2} \int_{0}^{\infty} \left [(t+x)(t+y)(t+z)  \right ]
          ^{-\frac{1}{2}}dt
  
      Parameters
      ----------
      x : ndarray
          First independent variable of the integral.
      y : ndarray
          Second independent variable of the integral.
      z : ndarray
          Third independent variable of the integral.
      errtol : float
          Error tolerance. Integral is computed with relative error less in
          magnitude than the defined value
  
      Returns
      -------
      RF : ndarray
          Value of the incomplete first order elliptic integral
  
      Notes
      -----
      x, y, and z have to be nonnegative and at most one of them is zero.
  
      References
      ----------
      .. [1] Carlson, B.C., 1994. Numerical computation of real or complex
             elliptic integrals. arXiv:math/9409227 [math.CA]
  
      """
      xn = x.copy()
      yn = y.copy()
      zn = z.copy()
      An = (xn + yn + zn) / 3.0
      Q = (3.0 * errtol) ** (-1 / 6.0) * np.max(
          np.abs([An - xn, An - yn, An - zn]), axis=0
      )
      # Convergence has to be done voxel by voxel
      index = ndindex(x.shape)
      for v in index:
          n = 0
          # Convergence condition
          while 4.0 ** (-n) * Q[v] > abs(An[v]):
              xnroot = np.sqrt(xn[v])
              ynroot = np.sqrt(yn[v])
              znroot = np.sqrt(zn[v])
              lamda = xnroot * (ynroot + znroot) + ynroot * znroot
              n = n + 1
              xn[v] = (xn[v] + lamda) * 0.250
              yn[v] = (yn[v] + lamda) * 0.250
              zn[v] = (zn[v] + lamda) * 0.250
              An[v] = (An[v] + lamda) * 0.250
  
      # post convergence calculation
      X = 1.0 - xn / An
      Y = 1.0 - yn / An
      Z = -X - Y
      E2 = X * Y - Z * Z
      E3 = X * Y * Z
      RF = An ** (-1 / 2.0) * (
          1
          - E2 / 10.0
          + E3 / 14.0
          + (E2**2) / 24.0
          - 3 / 44.0 * E2 * E3
      )
  
      return RF
  
imports: import numpy
  import warnings
  import scipy.optimize
  import dipy.core.sphere
  from dipy.reconst.multi_voxel import multi_voxel_fit
  from dipy.reconst.dti import TensorFit, mean_diffusivity, from_lower_triangular, lower_triangular, decompose_tensor, MIN_POSITIVE_SIGNAL, nlls_fit_tensor, restore_fit_tensor
  from dipy.reconst.utils import dki_design_matrix
  from dipy.reconst.recspeed import local_maxima
  from dipy.reconst.base import ReconstModel
  from dipy.core.ndindex import ndindex
  from dipy.core.geometry import sphere2cart, cart2sphere, perpendicular_directions
  from dipy.core.optimize import PositiveDefiniteLeastSquares
  from dipy.data import get_sphere, get_fnames, load_sdp_constraints
  from dipy.reconst.vec_val_sum import vec_val_vect
  from dipy.core.gradients import check_multi_b
label_desc: Use image node_id 2 for calling a global function with example usage: carlson_rf(x, y, z, errtol) and returns: RF