code: def _log_H_asymptotic(nu, kappa):
      
      beta = np.sqrt((nu + 0.5) ** 2)
      kappa_l = np.min([kappa, np.sqrt((3. * nu + 11. / 2.) * (nu + 3. / 2.))])
      return _S(kappa, nu + 0.5, beta) + (
          _S(kappa_l, nu, nu + 2.) - _S(kappa_l, nu + 0.5, beta)
      )
docs: Compute the Amos-type upper bound asymptotic approximation on H where
      log(H_\nu)(\kappa) = \int_0^\kappa R_\nu(t) dt.
  
      See "lH_asymptotic <-" in movMF.R and utility function implementation notes
      from https://cran.r-project.org/web/packages/movMF/index.html