AUXILIARY} \left[\begin{array}{cc}    \mathcal{J}^{LM}_{nlm,n'l'm'}\left(\zeta,\zeta',R_{AB},\xi_{C} \right)    \\   \mathcal{K}^{LM}_{nlm,n'l'm'}\left(\zeta,\zeta',R_{AB},\xi_{C} \right) \end{array} \right]