Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/256

$0=\left(1-m^{2}\right){\rm {A}}_{2}^{(5)}+{\frac {3m^{2}}{2}}{\frac {a}{a_{\text{ı}}}}$

$\times \left\{{\begin{aligned}1&+e^{2}+{\frac {\gamma ^{2}}{4}}+{\frac {9}{8}}e'^{2}+\left({\rm {B}}_{1}^{(7)}+{\rm {B}}_{1}^{(8)}\right){\frac {\gamma ^{2}}{m^{2}}}-{\frac {3}{2}}(1+2m){\rm {A}}_{2}^{(0)}\\\\&-{\frac {2(1-2m)(3-2m)(3-m)}{(2-3m)(2-m)}}{\rm {A}}_{2}^{(0)}-2{\rm {A}}_{2}^{(5)}-(2-3m){\rm {A}}_{2}^{(4)}\\\\&+{\rm {\left(B_{1}^{(9)}+B_{1}^{(10)}\right)B_{1}^{(0)}}}{\frac {\gamma ^{2}}{m^{2}}}-{\rm {A_{2}^{(5)}-11C_{2}^{(6)}-2C_{2}^{(9)}+2C_{2}^{(10)}}}\end{aligned}}\right\}$

$+6m\left[4{\rm {A_{2}^{(0)}+A_{2}^{(3)}-A_{2}^{(4)}-10A_{1}^{(1)}}}e^{2}+{\frac {5}{2}}\left({\rm {A_{1}^{(7)}-A_{1}^{(6)}}}\right)e^{2}\right],$

$0=\left[1-(2-m-c)^{2}\right]{\rm {A}}_{1}^{(6)}+{\frac {3}{2}}m^{2}{\frac {a}{a_{\text{ı}}}}$

$\times \left\{{\begin{aligned}{\frac {3+2m-c}{4}}+{\frac {2+m}{2-m-c}}-{\frac {3}{2}}{\rm {A}}_{1}^{(1)}-{\rm {A}}_{1}^{(6)}\\\\-\left({\frac {3+m+c}{2}}+{\frac {4}{2-m-c}}\right){\rm {A}}_{1}^{(9)}\end{aligned}}\right\}$

$0=\left[1-(2-3m-c)^{2}\right]{\rm {A}}_{1}^{(7)}-{\frac {3}{2}}m^{2}{\frac {a}{a_{\text{ı}}}}$

$\times \left\{{\begin{aligned}{\frac {7(3+6m-c}{4}}+{\frac {7(2+3m)}{2-3m-c}}+{\frac {3}{2}}{\rm {A}}_{1}^{(1)}\\\\+{\rm {A}}_{1}^{(7)}+\left({\frac {3-m-c}{2}}+{\frac {4}{2-3m-c}}\right){\rm {A}}_{1}^{(8)}\end{aligned}}\right\}$

$0=\left[1-(c+m)^{2}\right]{\rm {A}}_{1}^{(8)}-{\frac {3}{2}}m^{2}{\frac {a}{a_{\text{ı}}}}$

$\times \left\{{\begin{aligned}{\frac {3+2m}{2}}-\left({\frac {1+2m+c}{4}}+{\frac {2}{c+m}}\right){\rm {A}}_{1}^{(1)}\\\\+{\rm {A}}_{1}^{(8)}+\left({\frac {1+3m+c}{2}}+{\frac {4}{c+m}}\right){\rm {A}}_{1}^{(7)}\end{aligned}}\right\}$

$0=\left[1-(c-m)^{2}\right]{\rm {A}}_{1}^{(9)}-{\frac {3}{2}}m^{2}{\frac {a}{a_{\text{ı}}}}$

$\times \left\{{\begin{aligned}{\frac {3-2m}{2}}+{\rm {A}}_{1}^{(9)}+7\left({\frac {1+2m+c}{4}}+{\frac {2}{c-m}}\right){\rm {A}}_{1}^{(1)}\\\\+\left({\frac {1+m+c}{2}}+{\frac {4}{c-m}}\right){\rm {A}}_{1}^{(6)}\end{aligned}}\right\}$

$0=\left(1-4c^{2}\right){\rm {A}}_{2}^{(10)}+{\frac {3}{2}}m^{2}{\frac {a}{a_{\text{ı}}}}\left(1-{\rm {B}}_{0}^{(11)}{\frac {\gamma ^{2}}{m^{2}}}-{\rm {A}}_{2}^{(10)}\right),$

$0=\left[1-(2c-2+2m)^{2}\right]{\rm {A}}_{1}^{(11)}+{\frac {3}{4}}m^{2}{\frac {a}{a_{\text{ı}}}}$

$\times \left\{{\begin{aligned}{\frac {2+11m+8m^{2}}{2}}-{\frac {10+19m+8m^{2}}{2c-2+2m}}\\\\+4{\rm {A}}_{1}^{(1)}+{\frac {8{\rm {A}}_{1}^{(10)}+10({\rm {A}}_{1}^{(1)})^{2}}{2c-2+2m}}-2{\rm {A}}_{1}^{(11)}\end{aligned}}\right\}$

$0=\left(1-4g^{2}\right){\rm {A}}_{2}^{(12)}+{\frac {a}{a_{\text{ı}}}}\left(g^{2}-1-{\frac {3}{4}}{\frac {a-a_{\text{ı}}}{a}}+{\frac {3}{8}}m^{2}-{\frac {3}{2}}m^{2}{\rm {A}}_{2}^{(12)}\right),$

$0=\left[1-(2g-2+2m)^{2}\right]{\rm {A}}_{1}^{(13)}+{\frac {3}{4}}m^{2}{\frac {a}{a_{\text{ı}}}}$

$\times \left\{{\begin{aligned}{\frac {3+2m-2g}{4}}+{\frac {4g^{2}-1}{4(1-m)}}-{\frac {2+m}{2g-2+2m}}\\\\+{\frac {2{\rm {B}}_{1}^{(0)}}{m^{2}}}-2{\rm {A}}_{1}^{(13)}+{\frac {8{\rm {A}}_{2}^{(12)}}{2g-2+2m}}\end{aligned}}\right\}$

$0=\left(1-4m^{2}\right){\rm {A}}_{2}^{(14)}+{\frac {3}{2}}m^{2}{\frac {a}{a_{\text{ı}}}}\left({\frac {3}{2}}-{\rm {A}}_{2}^{(14)}\right).$