\begin{table}%ta1
\caption{\label{table:bigequations_scpi_powerlaw}The specific mass ratio distribution $\fq$ for pairing function SCP-I, resulting from a power-law generating mass distribution $f_m(m)$ and a uniform generating mass ratio distribution $h_q(q)$. See Appendix~\ref{appendix:scp_powerlaw} for details. }
%\centering
\begin{tabularx}{\textwidth}{p{0.1cm}XX}
  \hline \hline
  \mbox{SCP-I} & \multicolumn{1}{c}{Mass ratio distribution} & \multicolumn{1}{c}{Normalization constant} \\
  \hline
  \mbox{Case 1} &
\[
  f_q(q)=\left\{
  \begin{array}{ll}
    0 & 0< q< q_0 \\[2pt]
    k \left[1-(2c/x_2)^\gamma(1+q)^{-\gamma}\right] & q_0\leq q\leq 1\\
  \end{array}\right.
  \label{eq:fqscp1ex1ca1}
\]
&
\[
  k=\frac{1-\gamma}{(1-q_0)(1-\gamma)-2^{1-\gamma}(2c/x_2)^\gamma+2c/x_2}
  \label{eq:fscp1ex1ca1norm}
\]
\\
  \hline
\par
  \mbox{Case 2} &
\par
\[
  f_q(q)= k\left[1-(2c/x_2)^\gamma(1+q)^{-\gamma}\right] \quad 0< q\leq 1
  \label{eq:fqscp1ex1ca2}
\]
\par
&
\par
\[
  k=\frac{1-\gamma}{(1-\gamma)-(2c/x_2)^\gamma(2^{1-\gamma}-1)}
  \label{fqscp1ex1ca2norm}
\]
\par
\\
\par
  \hline
\par
  \mbox{Case 3} &
\par
\[
  f_q(q)=\left\{
  \begin{array}{ll}
    k\frac{1-(2c/x_2)^\gamma(1+q)^{-\gamma}}{1-(c/d)^\gamma} & 0< q\leq q_2\\[2pt]
    k & q_2< q\leq 1
  \end{array}\right.
  \label{eq:fqscp1ex1ca3}
\]
\par
&
\par
\begin{eqnarray*}
  k^{-1}=\frac{1}{1-(c/d)^\gamma}\left[q_2-\frac{(2c/x_2)^\gamma(
  (1+q_2)^{1-\gamma}-1)}{1-\gamma}\right]+1-q_2
  \label{fqscp1ex1ca3norm}
\end{eqnarray*}
\par
\\
\par
  \hline
\par
  \mbox{Case 4} &
\par
\[
  f_q(q)=\left\{
  \begin{array}{ll}
    0 & 0< q< q_0 \\[2pt]
    k\left[1-\left(\frac{2c}{x_2}\right)^\gamma(1+q)^{-\gamma}\right] & q_0\leq q< q_1\\[2pt]
    k\left[ \left(\frac{2c}{x_1}\right)^\gamma-\left(\frac{2c}{x_2}\right)^\gamma\right]
    (1+q)^{-\gamma} & q_1\leq q\leq 1\\
  \end{array}\right.
  \label{eq:fqscp1ex1ca4}
\]
\par
&
\par
\[
  k=\frac{1-\gamma}{2^{1-\gamma}[(2c/x_1)^\gamma-(2c/x_2)^\gamma]-\gamma(2c/x_1-2c/x_2)}
  \label{eq:fscp1ex1ca4norm}
\]
\par
\\
 \hline
\par
  \mbox{Case 5} &
\par
\[
  f_q(q)=\left\{
  \begin{array}{ll}
    k\left[1-\left(\frac{2c}{x_2}\right)^\gamma(1+q)^{-\gamma}\right] & 0< q< q_1\\[2pt]
    k\left[ \left(\frac{2c}{x_1}\right)^\gamma-\left(\frac{2c}{x_2}\right)^\gamma\right]
    (1+q)^{-\gamma} & q_1\leq q\leq 1\\
  \end{array}\right.
  \label{eq:fqscp1ex1ca5}
\]
\par
&
\par
\begin{eqnarray*}
  k= 
  \frac{1-\gamma}{q_1(1-\gamma)+[(2c/x_1)^\gamma-(2c/x_2)^\gamma]2^{1-\gamma}+(2c/x_2)^\gamma-2c/x_1}
  \label{eq:fscp1ex1ca5norm}
\end{eqnarray*}
\par
\\
\par
  \hline
\par
  \mbox{Case 6a} &
\par
\[
  f_q(q) =\left\{
  \begin{array}{ll}
    k\left[1-\left(\frac{2c}{x_2}\right)^\gamma(1+q)^{-\gamma}\right] & 0< q<q_1 \\[2pt]
    k\left[ \left(\frac{2c}{x_1}\right)^\gamma-\left(\frac{2c}{x_2}\right)^\gamma\right]
    (1+q)^{-\gamma} & q_1\leq q<q_2 \\[2pt]
    k\left[\left(\frac{2c}{x_1}\right)^\gamma(1+q)^{1-\gamma}-\left(\frac{c}{d}\right)^\gamma\right]
    & q_2\leq q\leq 1
  \end{array}\right.
  \label{eq:fqscp1ex1ca6a}
\]
\par
&
\par
\begin{eqnarray*}
  k &= &\frac{1-\gamma}{q_1(1-\gamma)-(2c/x_2)^\gamma\left[
  (1+q_1)^{1-\gamma}-1\right]}  \\ 
  && +\frac{1-\gamma}{\left[(2c/x_1)^\gamma-(2c/x_2)^\gamma\right]
  \left[(1+q_2)^{1-\gamma}-(1+q_1)^{1-\gamma}\right]}  \\ 
  &&+ \frac{1-\gamma}{(2c/x_1)^\gamma(2^{1-\gamma}-(1+q_2)^{1-\gamma}) -
  (c/d)^\gamma(1-q_2)(1-\gamma)}
  \label{eq:fscp1ex1ca6anorm}
\end{eqnarray*}
\par
\\
\par
  \hline
\par
  \mbox{Case 6b} &
\par
\[
  f_q(q) =\left\{
  \begin{array}{ll}
    k\left[1-\left(\frac{2c}{x_2}\right)^\gamma(1+q)^{-\gamma}\right] & 0< q<q_2 \\[2pt]
    k[1-\left(\frac{c}{d}\right)^\gamma] & q_2\leq q<q_1 \\[2pt]
    k\left[\left(\frac{2c}{x_1}\right)^\gamma(1+q)^{1-\gamma}-\left(\frac{c}{d}\right)^\gamma\right]
    & q_1\leq q\leq 1
  \end{array}\right.
  \label{eq:fqscp1ex1ca6b}
\]
\par
&
\par
\begin{eqnarray*}
    k&= & \frac{1-\gamma}{q_2(1-\gamma)-(2c/x_2)^\gamma\left[
    (1+q_2)^{1-\gamma}-1\right]}  \\ 
    &&+ \frac{1-\gamma}{(1-(c/d)^\gamma)(q_1-q_2)(1-\gamma)} \\ 
    &&+ \frac{1-\gamma}{(2c/x_1)^\gamma(2^{1-\gamma}-(1+q_1)^{1-\gamma}) -
    (c/d)^\gamma(1-q_1)(1-\gamma)}
  \label{eq:fscp1ex1ca6bnorm}
\end{eqnarray*}
\par
\\
\par
  \hline
\par
  \mbox{Case 7} &
\par
\[
  f_q(q)=k(1+q)^{-\gamma}
  \label{eq:fqscp1ex1ca7}
\]
\par
&
\par
\[
  k=\frac{1-\gamma}{2^{1-\gamma}-1} \quad \quad  \quad \quad \quad\quad\quad \quad  \quad \quad \quad\quad
\]
\par
\\
\par
  \hline
\par
  \mbox{Case 8} &
\par
\[
  f_q(q) =\left\{
  \begin{array}{ll}
    k\left[ \left(\frac{2c}{x_1}\right)^\gamma-\left(\frac{2c}{x_2}\right)^\gamma\right]
    (1+q)^{-\gamma} & 0<q<q_2 \\[2pt]
    k\left[\left(\frac{2c}{x_1}\right)^\gamma(1+q)^{1-\gamma}-\left(\frac{c}{d}\right)^\gamma\right]
    & q_2\leq q\leq 1
  \end{array}\right.
  \label{eq:fqscp1ex1ca8}
\]
\par
&
\par
\begin{eqnarray*}
    k&= & \frac{1-\gamma}{\left[(2c/x_1)^\gamma-(2c/x_2)^\gamma\right]
    \left[(1+q_2)^{1-\gamma}-1\right]}\\ 
    && +  \frac{1-\gamma}{(2c/x_1)^\gamma(2^{1-\gamma}-(1+q_2)^{1-\gamma})}
    \\ 
    && - \frac{1-\gamma}{(c/d)^\gamma(1-q_2)(1-\gamma)}
  \label{eq:fscp1ex1ca8norm}
\end{eqnarray*}
\par
\\
\par
 \hline
\par
  \mbox{Case 9} &
\par
\[
  f_q(q) =\left\{
  \begin{array}{ll}
    k\left[ \left(\frac{2c}{x_1}\right)^\gamma-\left(\frac{2c}{x_2}\right)^\gamma\right]
    (1+q)^{-\gamma} & 0<q<q_2 \\[2pt]
    k\left[\left(\frac{2c}{x_1}\right)^\gamma(1+q)^{1-\gamma}-\left(\frac{c}{d}\right)^\gamma\right]
    & q_2\leq q<q_3 \\[2pt]
    0 & q_3\leq q\leq 1
  \end{array}\right.
  \label{eq:fqscp1ex1ca9}
\]
\par
&
\par
\begin{eqnarray*}
  k&= & \frac{1-\gamma}{\left[(2c/x_1)^\gamma-(2c/x_2)^\gamma\right]
  \left[(1+q_2)^{1-\gamma}-1\right]}  \\ 
  & &+\frac{1-\gamma}{(2c/x_1)^\gamma( (1+q_3)^{1-\gamma}-(1+q_2)^{1-\gamma})} 
  \\ 
  && -\frac{1-\gamma}{(c/d)^\gamma(q_3-q_2)(1-\gamma)}
  \label{eq:fscp1ex1ca9norm}
\end{eqnarray*}
\par
\\
  \hline
\end{tabularx}
\par
\end{table}