code: def F_alternative(x, dim, dfd=np.inf, dfn=1):
      """
      Another way to compute F EC density as a product of a polynomial and a power
      of (1+x^2/m).
      """
      n = float(dfn)
      m = float(dfd)
      x = np.asarray(x, np.float64)
      p = polyF(dim=dim, dfd=dfd, dfn=dfn)
      v = p(np.sqrt(n * x))
      if np.isfinite(m):
          v *= np.power(1 + n * x / m, -(m + n - 2.0) / 2.0)
      else:
          v *= np.exp(-n * x / 2)
      v *= np.power(2 * np.pi, -(dim + 1) / 2.0)
      return v
  
imports: import numpy
  import scipy.stats
  from scipy.special import gammaln, hermitenorm
  import pytest
  from numpy.testing import assert_almost_equal
  from ..None import rft
label_desc: Use image node_id 5 for calling a global function with example usage: F_alternative(x, dim, dfd, dfn) and returns: v