code: def bethe_filling_zeroT(fermi_energy, hopping):
      
      fermi_energy = np.asarray(fermi_energy).clip(-2*hopping, 2*hopping)
      return 1/2. + fermi_energy/2 * bethe_lattice(fermi_energy, hopping) \
                      + np.arcsin(fermi_energy/2/hopping)/np.pi
docs: Returns the particle average count given a certan fermi energy, for the
         semicircular density of states of the bethe lattice