  In this paper, we derive asymptotic properties of both the velocity and the
vorticity fields to the 3-dimensional axially symmetric Navier-Stokes equations
at infinity under the generalized D-solution assumption
$\int_{\mathbb{R}^3}|\nabla u|^qdx<\infty$ for $2<q<\infty$. We do not impose
any zero or nonzero constant vector asymptotic assumption on the solution at
infinity. Our results generalize those in
\cite{CJ:2009JMFM,Ws:2018JMFM,CPZ2018} where the authors focused on the case
$q=2$ and the velocity field approaches zero at infinity. Meanwhile, when $q\to
2_+$ and the velocity field approaches zero at infinity, our results coincide
with the results in \cite{CJ:2009JMFM,Ws:2018JMFM,CPZ2018}.
