$\begin{figure} \par\includegraphics[width=9cm,clip]{fig4hure09682.eps} \end{figure}$ Figure 4: Potential ( plain lines) in a power-law disc with axis ratio $\Delta =0.1$ and $s=\{-2.5,-1.5,-0.5\}$ . The contribution of the power law, i.e. the term $A \varpi ^{1+s}$ in Eq. (33), is shown in comparison.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=9cm,clip]{fig5hure09682.eps} \end{figure}$ Figure 5: Coefficients A ( open circles), $A_\Delta$ ( triangles), and A₁ ( stars) versus the power-law exponent s of the surface density. A few remarkable exponents are shown ( open squares): the Mestel (infinite) disc with s=-1 (Mestel 1963), the Hayashi model for the solar nebula with s=-1.5 (Hayashi 1981), and the $\alpha$ and $\beta$ -viscosity discs where $s \approx -0.6$ depending on models (Richard & Zahn 1999; Collin-Souffrin & Dumont 1990; Dubrulle 1992; Shakura & Sunyaev 1973).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=9cm,clip]{fig7hure09682.eps}\end{figure}$ Figure 7: The exact potential for a power law disc with s=-1.5 ( thick line) compared to approximate values ( thin lines) found from Eq. (50) for N=0, 1, 2 and 3 (i.e. see Eqs. (52), (54), (55), etc.). The largest errors are found around edges.
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=9cm,clip]{fig8hure09682.eps}\end{figure}$ Figure 8: Contour map showing the decimal logarithm of the relative error in the potential in the $(\varpi ,s)$ -plane when $\psi$ is approximated by Eq. (53).
Open with DEXTER

In the text

$\begin{figure} \par\includegraphics[width=9cm,clip]{fig1hure09682.eps} \end{figure}$	Figure 1: Configuration for a finite-size flat disc.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=9cm,clip]{fig2hure09682.eps}\end{figure}$	Figure 2: Coefficient $\gamma _n$ versus n. Terms a_n and \|d_n\| versus n for s=-1.5.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=9cm,clip]{fig3hure09682.eps} \end{figure}$	Figure 3: Ranges of s where the edge surface density, edge potential and total disc mass are infinite.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=9cm,clip]{fig4hure09682.eps} \end{figure}$	Figure 4: Potential ( plain lines) in a power-law disc with axis ratio $\Delta =0.1$ and $s=\{-2.5,-1.5,-0.5\}$ . The contribution of the power law, i.e. the term $A \varpi ^{1+s}$ in Eq. (33), is shown in comparison.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=8.5cm,clip]{fig6hure09682.eps}\end{figure}$	Figure 6: Relative error in A when computed approximately from Eq. (48).
Open with DEXTER

$\begin{figure} \par\includegraphics[width=9cm,clip]{fig7hure09682.eps}\end{figure}$	Figure 7: The exact potential for a power law disc with s=-1.5 ( thick line) compared to approximate values ( thin lines) found from Eq. (50) for N=0, 1, 2 and 3 (i.e. see Eqs. (52), (54), (55), etc.). The largest errors are found around edges.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=9cm,clip]{fig8hure09682.eps}\end{figure}$	Figure 8: Contour map showing the decimal logarithm of the relative error in the potential in the $(\varpi ,s)$ -plane when $\psi$ is approximated by Eq. (53).
Open with DEXTER