<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\begin{eqnarray}
\mathcal{F}_{gq}^{[1_s]}(z,r)&amp;=&amp;\Bigl[\,9r(r+1)^3z^4-(r-1)(r+1)^2z^3-2(r+1)(19r+35)z^2
\nonumber\\
&amp;&amp;\hspace{0.2cm}-32(r+1)z-64\Bigr]\frac{16z}{27\left[(r+1)z-2\right]^2\left[(r+1)z+2\right]^3}\ln(z)
\nonumber\\
&amp;&amp;\hspace{-0.3cm}+\Bigl[\,(r+1)^3(21r+5)z^4+2(r+1)^2(5r+9)z^3+4(r+1)(23r-29)z^2
\nonumber\\
&amp;&amp;\hspace{0.2cm}+200(r+1)z-224\Bigr]\frac{2z\left[5z(r+1)-8\right]\ln\left(1+2\frac{1-z}{z(r+1)}\right)}{243\left[(r+1)z-2\right]^2\left[(r+1)z+2\right]^3}
\nonumber\\
&amp;&amp;\hspace{-0.3cm}+\Bigl[\,(r+1)^3(57r+41)z^4+4(r+1)^2(81r^2+61r-36)z^3
\nonumber\\
&amp;&amp;\hspace{0.2cm}-4(r+1)(55r+71)z^2-16(r+1)(81r+133)z+256\Bigr]
\nonumber\\
&amp;&amp;\hspace{0.2cm}\times\frac{4(1-z)}{243(r+1)\left[z^2(r+1)^2-4\right]^2}\,,
\label{Fgq1}
\end{eqnarray}

\begin{eqnarray}
\mathcal{F}_{gq}^{[8_s]}(z,r)&amp;=&amp;\Bigl[\,9r(r+1)^3z^4-4(r-1)(r+1)^2z^3-4(r+1)(11r+26)z^2
\nonumber\\
&amp;&amp;\hspace{0.2cm}-40(r+1)z-80\Bigr]\frac{32z\ln(z)}{27\left[(r+1)z-2\right]^2\left[(r+1)z+2\right]^3}
\nonumber\\
&amp;&amp;\hspace{-0.3cm}+\Bigl[\,(r+1)^4(33r+28)z^5-4(r+1)^3(37r-14)z^4
\nonumber\\
&amp;&amp;\hspace{0.2cm}+4(r+1)^2(47r-175)z^3+8(r+1)(33r+163)z^2
\nonumber\\
&amp;&amp;\hspace{0.2cm}-16(86r+131)z+1120\Bigr]\frac{8z\ln\left(1+2\frac{1-z}{z(r+1)}\right)}{243\left[(r+1)z-2\right]^2\left[(r+1)z+2\right]^3}
\nonumber\\
&amp;&amp;\hspace{-0.3cm}+\Bigl[\,(r+1)^3(24r+19)z^4+(r+1)^2(81r^2+56r-45)z^3
\nonumber\\
&amp;&amp;\hspace{0.2cm}-4(r+1)(11r+16)z^2-4(r+1)(81r+191)z+80\Bigr]
\nonumber\\
&amp;&amp;\hspace{0.2cm}\times\frac{32(1-z)}{243(r+1)\left[z^2(r+1)^2-4\right]^2}
\,,
\nonumber\\
\label{Fgq8s}
\end{eqnarray}

\begin{eqnarray}
\mathcal{F}_{gq}^{[8_a]}(z,r)&amp;=&amp;\Bigl[\,9(r-1)^2(r+1)^4z^6+(r+1)^3(67r^2-186r+67)z^5
\nonumber\\
&amp;&amp;\hspace{0.2cm}-(r+1)^2(13r^3+207r^2-81r-67)z^4
\nonumber\\
&amp;&amp;\hspace{0.2cm}-2(r+1)^2(85r^2+100r-233)z^3-36(r+1)(5r^2-6r-3)z^2
\nonumber\\
&amp;&amp;\hspace{0.2cm}+72(7r^2\hspace{-0.05cm}+\hspace{-0.05cm}18r+3)z\hspace{-0.05cm}+\hspace{-0.05cm}576r\Bigr]\frac{32\ln(z)}{27(r+1)^2\left[(r+1)z\hspace{-0.05cm}-\hspace{-0.05cm}2\right]^2\left[(r+1)z\hspace{-0.05cm}+\hspace{-0.05cm}2\right]^3}
\nonumber\\
&amp;&amp;\hspace{-0.3cm}-\Bigl[\,(r+1)^4(3r^3+35r^2+13r+13)z^6
\nonumber\\
&amp;&amp;\hspace{0.2cm}-2(r+1)^3(35r^3-195r^2+353r-57)z^5
\nonumber\\
&amp;&amp;\hspace{0.2cm}-8(r+1)^2(5r^3+125r^2-189r+91)z^4
\nonumber\\
&amp;&amp;\hspace{0.2cm}+16(r+1)(15r^3+7r^2+25r+97)z^3
\nonumber\\
&amp;&amp;\hspace{0.2cm}+16(19r^3+11r^2-227r-91)z^2+32(r^2+82r+17)z-1024r\Bigr]
\nonumber\\
&amp;&amp;\hspace{0.2cm}\times\frac{4\ln\left(1+2\frac{1-z}{z(r+1)}\right)}{27(r+1)^2\left[(r+1)z-2\right]^2\left[(r+1)z+2\right]^3}
\nonumber\\
&amp;&amp;\hspace{-0.3cm}+\Bigl[\,(r-1)(r+1)^3(21r^2-38r+37)z^6
\nonumber\\
&amp;&amp;\hspace{0.2cm}+4(r+1)^2(35r^3-324r^2+327r-82)z^5
\nonumber\\
&amp;&amp;\hspace{0.2cm}-8(r+1)(6r^3+75r^2+136r-93)z^4
\nonumber\\
&amp;&amp;\hspace{0.2cm}-16(18r^4+25r^3-104r^2+61r+44)z^3
\nonumber\\
&amp;&amp;\hspace{0.2cm}-16(36r^3-23r^2-214r-115)z^2+384(3r^2+r-1)z+2304r\Bigr]
\nonumber\\
&amp;&amp;\hspace{0.2cm}\times\frac{8(1-z)}{27(r+1)^2z\left[z(r-1)+2\right]\left[z^2(r+1)^2-4\right]^2}\,,
\label{Fgq8a}
\end{eqnarray}

\begin{eqnarray}
\mathcal{F}_{gq}^{[10]}(z,r)&amp;=&amp;\Bigl[\,(r+1)(r^2-6r+1)z^2-(r-1)(r^2+10r+1)z
\nonumber\\
&amp;&amp;\hspace{0.2cm}-2(r^2-2r-11)\Bigr]\frac{320z^3\ln(z)}{27\left[(r+1)z-2\right]^2\left[(r+1)z+2\right]^3}
\nonumber\\
&amp;&amp;\hspace{-0.3cm}-\Bigl[\,(r+1)^5z^4+2(r+1)(3r^3+9r^2-23r+3)z^3
\nonumber\\
&amp;&amp;\hspace{0.2cm}+4(r^3-21r^2+3r-7)z^2-8(r^2+6r-11)z-64\Bigr]
\nonumber\\
&amp;&amp;\hspace{0.2cm}\times\frac{40z^2\ln\left(1+2\frac{1-z}{z(r+1)}\right)}{27\left[(r+1)z-2\right]^2\left[(r+1)z+2\right]^3}
\nonumber\\
&amp;&amp;\hspace{-0.3cm}+\Bigl[\,(r-1)(r+1)^3z^4+2(3r-1)(r^2\hspace{-0.05cm}-\hspace{-0.05cm}10r+5)z^3+4(3r^2\hspace{-0.05cm}-\hspace{-0.05cm}20r+9)z^2
\nonumber\\
&amp;&amp;\hspace{0.2cm}+8(5r-7)z+64\Bigr]\frac{80z(1-z)}{27\left[z(r-1)+2\right]\left[z^2(r+1)^2-4\right]^2}
\,,
\label{Fgq10}
\end{eqnarray}

\begin{eqnarray}
\mathcal{F}_{gq}^{[27_s]}(z,r)&amp;=&amp;\Bigl[\,r(r+1)z^2-(r-1)z-6\Bigr]\frac{16z^3(r+1)^2\ln(z)}{\left[(r+1)z-2\right]^2\left[(r+1)z+2\right]^3}
\nonumber\\
&amp;&amp;\hspace{-0.3cm}+\Bigl[\,(r+1)^4z^4-2(r+1)^2(3r-1)z^3-4(r+1)(r+5)z^2
\nonumber\\
&amp;&amp;\hspace{0.2cm}+8(r+1)z-32\Bigr]\frac{2z^2(r+1)\ln\left(1+2\frac{1-z}{z(r+1)}\right)}{\left[(r+1)z-2\right]^2\left[(r+1)z+2\right]^3}
\nonumber\\
&amp;&amp;\hspace{-0.3cm}+\Bigl[\,(r+1)z^2+2(2r+1)z+8\Bigr]\frac{4z(1-z)(r+1)}{\left[z(r+1)+2\right]\left[z^2(r+1)^2-4\right]}
\,,
\label{Fgq27}
\end{eqnarray}

\begin{eqnarray}
\mathcal{F}_{q\overline{q}}^{[1_s]}(z,r)&amp;=&amp;-\Bigl[\,18r^2(r^2+1)z^4+(81r^3\hspace{-0.05cm}-\hspace{-0.05cm}35r^2+27r\hspace{-0.05cm}-\hspace{-0.05cm}1)z^3+4(38r^2\hspace{-0.05cm}-\hspace{-0.05cm}13r+3)z^2
\nonumber\\
&amp;&amp;\hspace{0.6cm}+4(31r-5)z+36\Bigr]\frac{8z\left[(9r+1)z+8\right]\ln\left(1+2\frac{1-z}{z(r+1)}\right)}{729(1-z)^2(rz+1)^3}
\nonumber\\
&amp;&amp;\hspace{-0.0cm}+\Bigl[\,18r^2(r^2\hspace{-0.05cm}-\hspace{-0.05cm}1)z^4+(81r^3+37r^2\hspace{-0.05cm}-\hspace{-0.05cm}27r+1)z^3+4(29r^2+14r-3)z^2
\nonumber\\
&amp;&amp;\hspace{0.6cm}+2(35r+11)z+16\Bigr]\frac{16\left[(9r+1)z+8\right]}{729(r+1)(1-z)\left[(r-1)z+2\right](rz+1)^2}\,,
\label{Fqq1}
\end{eqnarray}

\begin{eqnarray}
\mathcal{F}_{q\overline{q}}^{[8_s]}(z,r)&amp;=&amp;-\Bigl[\,9r^2(9r+4)(r^2+1)z^5+(477r^4+18r^3+130r^2+36r-13)z^4
\nonumber\\
&amp;&amp;\hspace{0.6cm}+(1143r^3-44r^2+125r+52)z^3+2(668r^2-53r-1)z^2
\nonumber\\
&amp;&amp;\hspace{0.6cm}+2(391r-14)z+180\Bigr]\frac{32z\ln\left(1+2\frac{1-z}{z(r+1)}\right)}{729(1-z)^2(rz+1)^3}
\nonumber\\
&amp;&amp;\hspace{-0.0cm}+\Bigl[\,9r^2(r^2-1)(9r+4)z^5+(477r^4+342r^3-104r^2-36r+13)z^4
\nonumber\\
&amp;&amp;\hspace{0.6cm}+(981r^3+640r^2-73r-52)z^3+2(479r^2+253r+14)z^2
\nonumber\\
&amp;&amp;\hspace{0.6cm}+40(11r+3)z+80\Bigr]\frac{64}{729(r+1)(1-z)\left[(r-1)z+2\right](rz+1)^2}\,,
\label{Fqq8s}
\end{eqnarray}

\begin{eqnarray}
\mathcal{F}_{q\overline{q}}^{[8_a]}(z,r)&amp;=&amp;\Bigl[\,2r^3(9r^4+35r^3+41r^2-19r-2)z^6
\nonumber\\
&amp;&amp;\hspace{0.2cm}+(88r^6+264r^5+309r^4-146r^3-26r^2-2r+1)z^5
\nonumber\\
&amp;&amp;\hspace{0.2cm}+2r(104r^4+213r^3+271r^2-65r-3)z^4
\nonumber\\
&amp;&amp;\hspace{0.2cm}+(349r^4+386r^3+492r^2\hspace{-0.05cm}-\hspace{-0.05cm}58r\hspace{-0.05cm}-\hspace{-0.05cm}1)z^3+4(99r^3+52r^2+63r\hspace{-0.05cm}-\hspace{-0.05cm}2)z^2
\nonumber\\
&amp;&amp;\hspace{0.2cm}+2(125r^2+26r+29)z+64r\Bigr]\frac{\ln\left(1+2\frac{1-z}{z(r+1)}\right)}{12(r-1)^2(1-z)^2(rz+1)^3}
\nonumber\\
&amp;&amp;\hspace{-0.3cm}-\Bigl[\,2r^2(r-1)(9r^3+35r^2+35r-3)z^5
\nonumber\\
&amp;&amp;\hspace{0.2cm}+(88r^5+200r^4+129r^3-191r^2+15r-1)z^4
\nonumber\\
&amp;&amp;\hspace{0.2cm}+2(107r^4+125r^3+140r^2-91r+3)z^3
\nonumber\\
&amp;&amp;\hspace{0.2cm}+(329r^3+165r^2+215r-53)z^2+2(141r^2+54r+25)z
\nonumber\\
&amp;&amp;\hspace{0.2cm}+48(2r+1)\Bigr]\frac{1}{6(r-1)^2(1-z)\left[(r-1)z+2\right](rz+1)^2}\,,
\label{Fqq8a}
\end{eqnarray}

\begin{eqnarray}
\mathcal{F}_{q\overline{q}}^{[10]}(z,r)&amp;=&amp;\Bigl[\,8r^4z^4-(r^4-22r^3+6r-1)z^3-2(r^3-13r^2-5r+1)z^2
\nonumber\\
&amp;&amp;\hspace{0.2cm}+16rz+8\Bigr]\frac{160z^2\ln\left(1+2\frac{1-z}{z(r+1)}\right)}{81(1-z)^2(rz+1)^3}
\nonumber\\
&amp;&amp;\hspace{-0.3cm}-\Bigl[\,8r^2(r-1)z^3-(r^3-23r^2+9r+1)z^2-2(r^2-12r+3)z
\nonumber\\
&amp;&amp;\hspace{0.2cm}-2(r-7)\Bigr]\frac{320z^2}{81(1-z)\left[(r-1)z+2\right](rz+1)^2}\,,
\label{Fqq10}
\end{eqnarray}

\begin{eqnarray}
\mathcal{F}_{q\overline{q}}^{[27_s]}(z,r)&amp;=&amp;-\Bigl[\,2r^2(r^2+1)z^4+(3r^2+1)(3r-1)z^3+4(4r^2-r+1)z^2
\nonumber\\
&amp;&amp;\hspace{0.6cm}+4(3r-1)z+4\Bigr]\frac{8z^2(r+1)\ln\left(1+2\frac{1-z}{z(r+1)}\right)}{3(1-z)^2(rz+1)^3}
\nonumber\\
&amp;&amp;\hspace{-0.0cm}+\Bigl[\,2r^2(r-1)z^3+(9r^2-4r+1)z^2+4(3r-1)z+6\Bigr]
\nonumber\\
&amp;&amp;\hspace{0.6cm}\times\frac{16z^2(r+1)}{3(1-z)\left[(r-1)z+2\right](rz+1)^2}\,.
\label{Fqq27}
\end{eqnarray}</pre></body></html>