def _log_H_asymptotic(nu, kappa):
beta = np.sqrt((nu + <NUM_LIT:0.5>) ** <NUM_LIT:2>)<EOL>kappa_l = np.min([kappa, np.sqrt((<NUM_LIT> * nu + <NUM_LIT> / <NUM_LIT>) * (nu + <NUM_LIT> / <NUM_LIT>))])<EOL>return _S(kappa, nu + <NUM_LIT:0.5>, beta) + (<EOL>_S(kappa_l, nu, nu + <NUM_LIT>) - _S(kappa_l, nu + <NUM_LIT:0.5>, beta)<EOL>)<EOL>
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