Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/269

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${\begin{aligned}{\rm {C}}_{0}^{(0)}=&{\frac {-2\left(1-{\frac {1}{4}}\gamma ^{2}\right)+{\frac {15m^{2}{\rm {A}}_{1}^{(1)}}{4(1-m)}}+3{\rm {A}}_{2}^{(0)}{\rm {A}}_{1}^{(1)}}{c}},\\\\{\rm {C}}_{0}^{(1)}=&{\frac {{\frac {3}{2}}+{\frac {1}{4}}e^{2}-{\frac {3}{4}}\gamma ^{2}-2{\rm {A}}_{2}^{(10)}}{2c}},\\\\{\rm {C}}_{0}^{(2)}=&-{\frac {1}{3c}},\\\\{\rm {C}}_{0}^{(3)}=&{\frac {{\frac {1}{2}}\left(1+{\frac {3}{2}}e^{2}-{\frac {1}{2}}\gamma ^{2}\right)-2{\rm {A}}_{2}^{(12)}+3{\rm {A}}_{0}^{(15)}e^{2}}{2g}},\\\\{\rm {C}}_{0}^{(4)}=&{\frac {-{\frac {3}{4}}-2{\rm {A}}_{0}^{(15)}}{2g-c}},\\\\{\rm {C}}_{0}^{(5)}=&-{\frac {\frac {3}{4}}{2g+c}},\\\\{\rm {C}}_{2}^{(6)}=&{\frac {\left\{{\begin{aligned}&{\frac {-3m^{2}\left(1+2e^{2}-{\frac {5}{2}}e'^{2}\right)}{4(1-m)}}\\&\qquad -3m^{2}e^{2}\left({\frac {1+m}{2-2m-c}}+{\frac {1-m}{2-2m+c}}\right)\\&-2{\rm {A}}_{2}^{(0)}\left(1+{\frac {1}{2}}e^{2}-{\frac {1}{4}}\gamma ^{2}\right)+3e^{2}{\rm {A}}_{1}^{(1)}+3e^{2}{\rm {A}}_{2}^{(2)}\end{aligned}}\right\}}{2-2m}},\\\\{\rm {C}}_{1}^{(7)}=&{\frac {\left\{{\begin{aligned}&{\frac {3m^{2}\left(1+2e^{2}-{\frac {1}{4}}\gamma ^{2}-{\frac {5}{2}}e'^{2}\right)}{4(1-m)}}\\&\qquad +{\frac {3m^{2}(1+m)\left(1+{\frac {3}{4}}e^{2}-{\frac {1}{4}}\gamma ^{2}-{\frac {5}{2}}e'^{2}\right)}{2-2m+c}}\\&-{\frac {3m^{2}e^{2}\left(10+19m+18m^{2}\right)}{8(2c-2+2m)}}\\&\qquad -2{\rm {A}}_{1}^{(1)}\left(1+{\frac {1}{2}}e^{2}-{\frac {1}{4}}\gamma ^{2}\right)+3{\rm {A}}_{2}^{(0)}+3e^{2}{\rm {A}}_{1}^{(11)}\end{aligned}}\right\}}{2-2m-c}},\\\\{\rm {C}}_{2}^{(8)}=&{\frac {{\frac {3m^{2}}{4(1-m)}}+{\frac {3m^{2}(1-m)}{2-2m+c}}-2{\rm {A}}_{2}^{(2)}+3{\rm {A}}_{2}^{(0)}-3{\rm {A}}_{1}^{(1)}e^{2}}{2-2m+c}},\\\\{\rm {C}}_{2}^{(9)}=&{\frac {{\frac {3m^{2}}{4(2-m)}}-2{\rm {A}}_{2}^{(3)}+3{\rm {A}}_{1}^{(6)}e^{2}}{2-m}},\\\\{\rm {C}}_{2}^{(10)}=&{\frac {-{\frac {21m^{2}}{4(2-3m)}}-2{\rm {A}}_{2}^{(4)}+3{\rm {A}}_{1}^{(7)}e^{2}}{2-3m}},\end{aligned}}$