  For a particular generalised-NFW (gNFW) mass distribution, we derive
analytical expressions for its surface mass density, projected mass, and
deflection potential, given in terms of three representations of the Fox
$H$-function, for which we provide their corresponding power (logarithmic)
series expansions. They are handy in computationally intensive tasks. From
these results, we obtain closed-form expressions for the super-NFW (sNFW) in
terms of complete elliptic functions, which have not yet been reported in the
literature. Additionally, we find that, for a fixed $\kappa_0$ (characteristic
convergence), when the number of images is maximal (three for the sNFW), the
sum of their signed magnification, named $I_{\text{sNFW}}$, varies with the
position of the source $y$ inside the radial caustic $y_{\text{c2}}$. The
higher variations occur for $\kappa_0\lesssim 1$, while $I_{\text{sNFW}}$ can
be considered as constant when $\kappa_0$ is approximately within the range
2-10. This range can be extended depending on the observational uncertainties,
since for higher values of $\kappa_0$, the variations in $I_{\text{sNFW}}$ are
relatively small. This behaviour is shared with the NFW and Hernquist lenses.
