def _fractional_power_superdiag_entry(l1, l2, t12, p):
    if l1 == l2:
        f12 = t12 * p * l1**(p-1)
    elif abs(l1) < abs(l2) / 2 or abs(l2) < abs(l1) / 2:
        f12 = t12 * ((l2**p) - (l1**p)) / (l2 - l1)
    else:
        # This is Eq. (5.5) in [1].
        z = (l2 - l1) / (l2 + l1)
        log_l1 = np.log(l1)
        log_l2 = np.log(l2)
        arctanh_z = np.arctanh(z)
        tmp_a = t12 * np.exp((p/2)*(log_l2 + log_l1))
        tmp_u = _unwindk(log_l2 - log_l1)
        if tmp_u:
            tmp_b = p * (arctanh_z + np.pi * 1j * tmp_u)
        else:
            tmp_b = p * arctanh_z
        tmp_c = 2 * np.sinh(tmp_b) / (l2 - l1)
        f12 = tmp_a * tmp_c
    return f12
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