\begin{table}%TB.1
\caption{\label{table:ainfty}Values of $A$ ($4$th column) computed within the computer precision (double precision; about $16$-digit) for different power law exponents $s$ or $s'$ (Cols $1$ to $3$) including those relevant for astrophysical applications (see also Fig.~\ref{fig:ainfty.eps}). Also given are the relative error on the coefficient ($5$th column) and the number of iterations ($6$th column) required.}
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\begin{tabular}{ccccccl}
\hline\hline
$s$ & $-3-s$ & $s'$ & Coefficient $A$ & Relative error & Iterations & Comment \\
\hline
{\tt -4.00} & {\tt +1.00} & {\tt -2.50} & {\tt -9.65735902799760E-02} & {\tt +3.1E-15 }& {\tt  6200} &  values of $A_\Delta$ and $A_1$\\
 {\tt -3.95} & {\tt +0.95} & {\tt -2.45} & {\tt -5.08795971306598E+00} & {\tt +1.6E-16 }& {\tt  4763}\\
 {\tt -3.90} & {\tt +0.90} & {\tt -2.40} & {\tt -2.57897148688964E+00} & {\tt +9.9E-17 }& {\tt  6289}\\
 {\tt -3.85} & {\tt +0.85} & {\tt -2.35} & {\tt -1.73622548292480E+00} & {\tt +3.9E-17 }& {\tt  8653}\\
 {\tt -3.80} & {\tt +0.80} & {\tt -2.30} & {\tt -1.30966680644896E+00} & {\tt +2.1E-17 }& {\tt 10760}\\
 {\tt -3.75} & {\tt +0.75} & {\tt -2.25} & {\tt -1.04923490407066E+00} & {\tt +8.1E-17 }& {\tt  7977}\\
 {\tt -3.70} & {\tt +0.70} & {\tt -2.20} & {\tt -8.71529232712215E-01} & {\tt +1.4E-16 }& {\tt  7154}\\
 {\tt -3.65} & {\tt +0.65} & {\tt -2.15} & {\tt -7.40760471984439E-01} & {\tt +2.1E-16 }& {\tt  6696}\\
 {\tt -3.60} & {\tt +0.60} & {\tt -2.10} & {\tt -6.38987239513759E-01} & {\tt +2.8E-16 }& {\tt  6379}\\
 {\tt -3.55} & {\tt +0.55} & {\tt -2.05} & {\tt -5.56193814181879E-01} & {\tt +3.5E-16 }& {\tt  6133}\\
 {\tt -3.50} & {\tt +0.50} & {\tt -2.00} & {\tt -4.86319914494768E-01} & {\tt +4.3E-16 }& {\tt  5926}\\
 {\tt -3.45} & {\tt +0.45} & {\tt -1.95} & {\tt -4.25454571886386E-01} & {\tt +5.2E-16 }& {\tt  5743}\\
 {\tt -3.40} & {\tt +0.40} & {\tt -1.90} & {\tt -3.70931368062394E-01} & {\tt +6.3E-16 }& {\tt  5576}\\
 {\tt -3.35} & {\tt +0.35} & {\tt -1.85} & {\tt -3.20839275213352E-01} & {\tt +7.7E-16 }& {\tt  5420}\\
 {\tt -3.30} & {\tt +0.30} & {\tt -1.80} & {\tt -2.73740796314985E-01} & {\tt +9.4E-16 }& {\tt  5270}\\
 {\tt -3.25} & {\tt +0.25} & {\tt -1.75} & {\tt -2.28500045775376E-01} & {\tt +1.2E-15 }& {\tt  5124}\\
 {\tt -3.20} & {\tt +0.20} & {\tt -1.70} & {\tt -1.84171894656878E-01} & {\tt +1.5E-15 }& {\tt  4980}\\
 {\tt -3.15} & {\tt +0.15} & {\tt -1.65} & {\tt -1.39926048201652E-01} & {\tt +2.0E-15 }& {\tt  4837}\\
 {\tt -3.10} & {\tt +0.10} & {\tt -1.60} & {\tt -9.49911954664950E-02} & {\tt +3.1E-15 }& {\tt  4694}\\
 {\tt -3.05} & {\tt +0.05} & {\tt -1.55} & {\tt -4.86101640289562E-02} & {\tt +6.3E-15 }& {\tt  4550}\\
 {\tt -3.00} & {\tt +0.00} & {\tt -1.50} & {\tt -8.70956628336228E-15} & {\tt +3.6E-02 }& {\tt  4403} & strictly $0$ (see Appendix \ref{app:azero})\\
 {\tt -2.95} & {\tt -0.05} & {\tt -1.45} & {\tt +5.16876888183838E-02} & {\tt +6.4E-15 }& {\tt  4252}\\
 {\tt -2.90} & {\tt -0.10} & {\tt -1.40} & {\tt +1.07410381098617E-01} & {\tt +3.2E-15 }& {\tt  4098}\\
 {\tt -2.85} & {\tt -0.15} & {\tt -1.35} & {\tt +1.68286941322651E-01} & {\tt +2.1E-15 }& {\tt  3937}\\
 {\tt -2.80} & {\tt -0.20} & {\tt -1.30} & {\tt +2.35664501680007E-01} & {\tt +1.6E-15 }& {\tt  3771}\\
 {\tt -2.75} & {\tt -0.25} & {\tt -1.25} & {\tt +3.11208301380443E-01} & {\tt +1.2E-15 }& {\tt  3596}\\
 {\tt -2.70} & {\tt -0.30} & {\tt -1.20} & {\tt +3.97027142932255E-01} & {\tt +1.0E-15 }& {\tt  3410}\\
 {\tt -2.65} & {\tt -0.35} & {\tt -1.15} & {\tt +4.95854560428368E-01} & {\tt +8.6E-16 }& {\tt  3212}\\
 {\tt -2.60} & {\tt -0.40} & {\tt -1.10} & {\tt +6.11318936974807E-01} & {\tt +7.4E-16 }& {\tt  2997}\\
 {\tt -2.55} & {\tt -0.45} & {\tt -1.05} & {\tt +7.48359798181055E-01} & {\tt +6.5E-16 }& {\tt  2759}\\
 {\tt -2.50} & {\tt -0.50} & {\tt -1.00} & {\tt +9.13893162088934E-01} & {\tt +5.7E-16 }& {\tt  2486}\\
 {\tt -2.45} & {\tt -0.55} & {\tt -0.95} & {\tt +1.11792019234452E+00} & {\tt +5.1E-16 }& {\tt  2151}\\
 {\tt -2.40} & {\tt -0.60} & {\tt -0.90} & {\tt +1.37546760819327E+00} & {\tt +4.5E-16 }& {\tt  1662}\\
 {\tt -2.35} & {\tt -0.65} & {\tt -0.85} & {\tt +1.71019225943660E+00} & {\tt +4.1E-16 }& {\tt  1335}\\
 {\tt -2.30} & {\tt -0.70} & {\tt -0.80} & {\tt +2.16159222263118E+00} & {\tt +3.7E-16 }& {\tt  1821}\\
 {\tt -2.25} & {\tt -0.75} & {\tt -0.75} & {\tt +2.80087471242395E+00} & {\tt +3.4E-16 }& {\tt  1997}\\
 {\tt -2.20} & {\tt -0.80} & {\tt -0.70} & {\tt +3.77063202688011E+00} & {\tt +3.1E-16 }& {\tt  2058}\\
 {\tt -2.15} & {\tt -0.85} & {\tt -0.65} & {\tt +5.40388067136072E+00} & {\tt +2.8E-16 }& {\tt  2036}\\
 {\tt -2.10} & {\tt -0.90} & {\tt -0.60} & {\tt +8.70024086898869E+00} & {\tt +2.6E-16 }& {\tt  1928}\\
 {\tt -2.05} & {\tt -0.95} & {\tt -0.55} & {\tt +1.86592556634413E+01} & {\tt +2.4E-16 }& {\tt  1681}\\
  {\tt -2.00} & {\tt -1.00} & {\tt -0.50} & {\tt -1.38629436111989E+00} & {\tt +7.2E-18 }& {\tt  7955} &  values of $A_\Delta$ and $A_1$ \\
 {\tt -1.95} & {\tt -1.05} & {\tt -0.45} & {\tt -2.14370823367682E+01} & {\tt +2.1E-16 }& {\tt  1770}\\
 {\tt -1.90} & {\tt -1.10} & {\tt -0.40} & {\tt -1.14939346514465E+01} & {\tt +1.9E-16 }& {\tt  2141}\\
 {\tt -1.85} & {\tt -1.15} & {\tt -0.35} & {\tt -8.22454216651923E+00} & {\tt +1.8E-16 }& {\tt  2399}\\
 {\tt -1.80} & {\tt -1.20} & {\tt -0.30} & {\tt -6.63018820764787E+00} & {\tt +1.7E-16 }& {\tt  2598}\\
 {\tt -1.75} & {\tt -1.25} & {\tt -0.25} & {\tt -5.71250114438470E+00} & {\tt +1.7E-16 }& {\tt  2755}\\
 {\tt -1.70} & {\tt -1.30} & {\tt -0.20} & {\tt -5.14024384191494E+00} & {\tt +1.6E-16 }& {\tt  2878}\\
 {\tt -1.65} & {\tt -1.35} & {\tt -0.15} & {\tt -4.77330268633758E+00} & {\tt +1.6E-16 }& {\tt  2972}\\
 {\tt -1.60} & {\tt -1.40} & {\tt -0.10} & {\tt -4.54390925876444E+00} & {\tt +1.5E-16 }& {\tt  3039}\\
 {\tt -1.55} & {\tt -1.45} & {\tt -0.05} & {\tt -4.41737401180816E+00} & {\tt +1.5E-16 }& {\tt  3078}\\
 {\tt -1.50} & {\tt -1.50} & {\tt +0.00} & {\tt -4.37687923045294E+00} & {\tt +1.5E-16 }& {\tt  3091}\\
 {\tt -1.45} & {\tt -1.55} & {\tt +0.05} & {\tt -4.41737401180816E+00} & {\tt +1.5E-16 }& {\tt  3078}\\
 \hline
\end{tabular}
\end{table}