# Template:LSU CT99CommonTheme1

 $~\Phi(\varpi,z)\biggr|_\mathrm{axisym}$ $~=$ $~ - \frac{G}{\pi} \iint\limits_\mathrm{config} \biggl[ \frac{\mu}{(\varpi~ \varpi^')^{1 / 2}} \biggr] K(\mu) \rho(\varpi^', z^') 2\pi \varpi^'~ d\varpi^' dz^'$ $\mathrm{where:}~~~\mu \equiv \{4\varpi \varpi^' /[ (\varpi+\varpi^')^2 + (z-z^')^2]\}^{1 / 2}$
and, $~K(\mu)$ is the complete elliptic integral of the first kind. This Key Equation may be straightforwardly obtained, for example, by combining Eqs. (31), (32b), and (24) from Cohl & Tohline (1999); see also, Bannikova et al. (2011), Trova, Huré & Hersant (2012), and Fukushima (2016).