\begin{table}%Ta2
\caption{\label{table:bigequations_scpii_powerlaw}The specific mass ratio distribution $\fq$ for pairing function SCP-II, resulting from a power-law generating mass distribution $f_{\rm m}(m)$ and a uniform generating mass ratio distribution $h_q(q)$. See Appendix~\ref{appendix:scp_powerlaw} for details. }
\par
\small%\centering
\par
\begin{tabularx}{\textwidth}{p{0.01cm}XX}
\hline\hline
  \mbox{SCP-II} & \multicolumn{1}{c}{Mass ratio distribution} & \multicolumn{1}{c}{Normalization constant} \\
  \hline
\par
  \mbox{Case 1} &
\par
\[
  f_q(q) =\left\{
  \begin{array}{ll}
    0 & 0< q<\frac{c}{x_2} \\[3pt]
    k\left[ \left(\frac{2q}{1+q}\right)^\gamma - \left(\frac{2c/x_2}{1+q}\right)^{\gamma}
    \right]& \frac{c}{x_2}\leq q<\frac{c}{x_1} \\[3pt]
    k\left[ \left(\frac{2c}{x_1}\right)^\gamma-
    \left(\frac{2c}{x_2}\right)^\gamma\right](1+q)^{-\gamma} & \frac{c}{x_1}\leq q\leq 1
  \end{array}\right.
  \label{eq:fqscp2ex1ca1}
\]
\par
&
\par
\begin{eqnarray*}
  k^{-1} & =& \int_{c/x_2}^{c/x_1}\left(\frac{2q}{1+q}\right)^\gamma {\rm d}q -
  \frac{(2c/x_2)^\gamma}{1-\gamma}\left[
  \left(1+\frac{c}{x_1}\right)^{1-\gamma} -
  \left(1+\frac{c}{x_2}\right)^{1-\gamma}\right] \\[3pt]
  & &+\frac{(2c/x_1)^\gamma-(2c/x_2)^\gamma}{1-\gamma}
  \left[2^{1-\gamma}-\left(1+\frac{c}{x_1}\right)^{1-\gamma}\right]
  \label{eq:fqscp2ex1ca1norm}
\end{eqnarray*}
\par
\\
\par
   \hline
\par
  \mbox{Case 2a} &
\par
\[
  f_q(q) =\left\{
  \begin{array}{ll}
    0 & 0< q<\frac{c}{x_2} \\[3pt]
    k\left[ \left(\frac{2q}{1+q}\right)^\gamma -
    \left(\frac{2c/x_2}{1+q}\right)^\gamma\right] & \frac{c}{x_2}\leq q <q_2 \\[3pt]
    k\left[ \left(\frac{2q}{1+q}\right)^\gamma - \left(\frac{c}{d}\right)^\gamma\right]
    & q_2\leq q< \frac{c}{x_1} \\[3pt]
    k\left[ \left(\frac{2c/x_1}{1+q}\right)^\gamma
    -\left(\frac{c}{d}\right)^\gamma\right] & \frac{c}{x_1}\leq q\leq 1
  \end{array}\right.~.
  \label{eq:fqscp2ex1ca2a}
\]
\par
&
\par
  \begin{eqnarray*}
    k^{-1}& =  &\int_{c/x_2}^{c/x_1}\left(\frac{2q}{1+q}\right)^\gamma {\rm d}q 
    \\[3pt]
    &&- \frac{(2c/x_2)^\gamma}{1-\gamma}\left[
    (1+q_2)^{1-\gamma}-\left(1+\frac{c}{x_2}\right)^{1-\gamma}\right] 
    \\[3pt]
    &&+ \frac{(2c/x_1)^\gamma}{1-\gamma}\left[2^{1-\gamma}-\left(1+\frac{c}{x_1}\right)^{1-\gamma}\right]
    - \left(\frac{c}{d}\right)^\gamma(1-q_2)
  \end{eqnarray*}
  \label{eq:fqscp2ex1ca2anorm}
\par
\\
  \hline
\par
  \mbox{Case 2b} &
\par
\[
  f_q(q) =\left\{
  \begin{array}{ll}
    0 & 0< q<\frac{c}{x_2} \\[3pt]
    k\left[ \left(\frac{2q}{1+q}\right)^\gamma -
    \left(\frac{2c/x_2}{1+q}\right)^\gamma\right]  & \frac{c}{x_2}\leq q <\frac{c}{x_1} \\[3pt]
    k\left[ \left(\frac{2c}{x_1}\right)^\gamma-\left(\frac{2c}{x_2}\right)^\gamma\right](1+q)^{-\gamma} & \frac{c}{x_1}\leq q< q_2 \\[3pt]
    k\left[ \left(\frac{2c/x_1}{1+q}\right)^\gamma -\left(\frac{c}{d}\right)^\gamma\right] & q_2\leq q\leq 1
  \end{array}\right.~.
  \label{eq:fqscp2ex1ca2b}
\]
\par
&
\par
  \begin{eqnarray*}
    k^{-1}  &= &\int_{c/x_2}^{c/x_1}\left(\frac{2q}{1+q}\right)^\gamma {\rm d}q\\[3pt]
    & &- \frac{(2c/x_2)^\gamma}{1-\gamma}\left[
    \left(1+\frac{c}{x_1}\right)^{1-\gamma}-\left(1+\frac{c}{x_2}\right)^{1-\gamma}\right]  \\[3pt]
    && +\frac{(2c/x_1)^\gamma-(2c/x_2)^\gamma}{1-\gamma}
    \left[ (1+q_2)^{1-\gamma}-\left(1+\frac{c}{x_1}\right)^{1-\gamma}\right]  \\[3pt]
    &&+ \frac{(2c/x_1)^\gamma}{1-\gamma}\left[2^{1-\gamma}-(1+q_2)^{1-\gamma}\right]
    - \left(\frac{c}{d}\right)^\gamma(1-q_2)
  \end{eqnarray*}
  \label{eq:fqscp2ex1ca2bnorm} 
\par
\\
\par
  \hline
\par
  \mbox{Case 3a} &
\par
\[
  f_q(q) =\left\{
  \begin{array}{ll}
    0 & 0< q<\frac{c}{x_2} \\[3pt]
    k\left[ \left(\frac{2q}{1+q}\right)^\gamma -
    \left(\frac{2c/x_2}{1+q}\right)^\gamma\right] & \frac{c}{x_2}\leq q <q_2 \\[3pt]
    k\left[ \left(\frac{2q}{1+q}\right)^\gamma - \left(\frac{c}{d}\right)^\gamma\right] & q_2\leq q< \frac{c}{x_1} \\[3pt]
    k\left[ \left(\frac{2c/x_1}{1+q}\right)^\gamma
    -\left(\frac{c}{d}\right)^\gamma\right] & \frac{c}{x_1}\leq q< q_3\\[3pt]
    0 & q_3\leq q\leq 1
  \end{array}\right.
  \label{eq:fqscp2ex1ca3a}
\]
\par
&
\par
  \begin{eqnarray*} 
    k^{-1} & =& \int_{c/x_2}^{c/x_1}\left(\frac{2q}{1+q}\right)^\gamma {\rm d}q\\[3pt]
    & &- \frac{(2c/x_2)^\gamma}{1-\gamma}\left[
    (1+q_2)^{1-\gamma}-\left(1+\frac{c}{x_2}\right)^{1-\gamma}\right] \\[3pt]
    & &+ \frac{(2c/x_1)^\gamma}{1-\gamma}
    \left[(1+q_3)^{1-\gamma}-\left(1+\frac{c}{x_1}\right)^{1-\gamma}\right]
    - \left(\frac{c}{d}\right)^\gamma(q_3-q_2)
  \end{eqnarray*}
  \label{eq:fqscp2ex1ca3anorm}
\par
\\
\par
  \hline
\par
  \mbox{Case 3b} &
\par
\[
  f_q(q) =\left\{
  \begin{array}{ll}
    0 & 0< q<\frac{c}{x_2} \\[3pt]
    k\left[ \left(\frac{2q}{1+q}\right)^\gamma -
    \left(\frac{2c/x_2}{1+q}\right)^\gamma\right]  & \frac{c}{x_2}\leq q <\frac{c}{x_1} \\[3pt]
    k\left[ \left(\frac{2c/x_1}{1+q}\right)^\gamma-\left(\frac{2c/x_2}{1+q}\right)^\gamma\right] &
    \frac{c}{x_1}\leq q< q_2 \\[3pt]
    k\left[ \left(\frac{2c/x_1}{1+q}\right)^\gamma -\left(\frac{c}{d}\right)^\gamma\right] & q_2\leq q<q_3 \\[3pt]
    0 & q_3\leq q\leq 1
  \end{array}\right.
  \label{eq:fqscp2ex1ca3b}
\]
\par
&
\par
  \begin{eqnarray*} 
    k^{-1} & =& \int_{c/x_2}^{c/x_1}\left(\frac{2q}{1+q}\right)^\gamma {\rm d}q \\[3pt]
   & &-\frac{(2c/x_2)^\gamma}{1-\gamma}\left[
    \left(1+\frac{c}{x_1}\right)^{1-\gamma}-\left(1+\frac{c}{x_2}\right)^{1-\gamma}\right] \\[3pt]
   &&+  \frac{(2c/x_1)^\gamma-(2c/x_2)^\gamma}{1-\gamma}
    \left[ (1+q_2)^{1-\gamma}-\left(1+\frac{c}{x_1}\right)^{1-\gamma}\right] \\[3pt]
    &&+ \frac{(2c/x_1)^\gamma}{1-\gamma}\left[(1+q_3)^{1-\gamma}-(1+q_2)^{1-\gamma}\right]
    - \left(\frac{c}{d}\right)^\gamma(q_3-q_2)
  \end{eqnarray*}
  \label{eq:fqscp2ex1ca3bnorm}
\par
\\
\par
  \hline
\end{tabularx}
\par
\end{table}