def METHOD_NAME(nu: int, m: complex, alpha: float) -> float:
    J_nu_alpha = jv(nu, alpha)
    J_nu_malpha = jv(nu, m * alpha)
    J_nu_alpha_p = jvp(nu, alpha, 1)
    J_nu_malpha_p = jvp(nu, m * alpha, 1)
    H_nu_alpha = hankel2(nu, alpha)
    H_nu_alpha_p = h2vp(nu, alpha, 1)
    a_nu_num = J_nu_alpha * J_nu_malpha_p - m * J_nu_malpha * J_nu_alpha_p
    a_nu_den = H_nu_alpha * J_nu_malpha_p - m * J_nu_malpha * H_nu_alpha_p
    return a_nu_num / a_nu_den