Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/251

$+{\frac {3m^{2}}{2a_{\text{ı}}}}\left(1-{\rm {B}}_{0}^{(11)}{\frac {\gamma ^{2}}{m^{2}}}-{\rm {A}}_{2}^{(10)}\right)e^{2}\cos(2v-2\varpi )$

$+{\frac {3m^{2}}{4a_{\text{ı}}}}\left\{{\begin{aligned}&{\frac {2+11m+8m}{2}}-{\frac {10+19m+8m^{2}}{2c-2+2m}}\\\\&\quad +4{\rm {A}}_{1}^{(1)}+{\frac {8{\rm {A}}_{2}^{(10)}+10\left({\rm {A}}_{1}^{(1)}\right)^{2}}{2c-2+2m}}-2{\rm {A}}_{1}^{(11)}\end{aligned}}\right\}$

$\times e^{2}\cos(2cv-2v+2mv-2\varpi )$

$-{\frac {3}{4a_{\text{ı}}}}\left(1+e^{2}-{\frac {\gamma ^{2}}{4}}-{\frac {1}{2}}m^{2}+2m^{2}{\rm {A}}_{2}^{(12)}\right)\gamma ^{2}\cos(2gv-2\theta )$

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

$\times \gamma ^{2}\cos(2gv-2v+2mv-2\theta )$

$+{\frac {3m^{2}}{2a_{\text{ı}}}}\left({\frac {3}{2}}-{\rm {A}}_{2}^{(14)}\right)e'^{2}\cos(2c'mv-2\varpi ')$

$-{\frac {3m^{2}}{2a_{\text{ı}}}}\left\{{\begin{aligned}&{\frac {1}{2}}+{\frac {{\rm {B}}_{2}^{(3)}}{m^{2}}}+{\frac {1+c-2g-10m}{4}}{\rm {A}}_{1}^{(1)}-(10+5m){\rm {A}}_{1}^{(13)}\\\\&\quad +(5+m){\rm {A}}_{1}^{(16)}-{\frac {{\rm {B}}_{1}^{(0)}{\rm {B}}_{2}^{(5)}}{m^{2}}}+{\rm {A}}_{0}^{(15)}\end{aligned}}\right\}$

$\times e\gamma ^{2}\cos(2gv-cv-2\theta +\varpi )$

$-{\frac {3m^{2}}{4a_{\text{ı}}}}\left\{{\begin{aligned}&1+2m+{\frac {5+m}{1-2m}}+{\frac {3(1-m)}{3-2m}}+2{\rm {A}}_{1}^{(16)}\\\\&\quad -{\frac {2{\rm {B}}_{2}^{(4)}}{m^{2}}}+{\frac {10{\rm {A}}_{0}^{(15)}}{1-2m}}\end{aligned}}\right\}$

$\times e\gamma ^{2}\cos(2v-2mv-2gv+cv+2\theta -\varpi )$

$+{\frac {m^{2}}{a_{\text{ı}}}}\left\{{\begin{aligned}&{\frac {9}{8}}(1-2\mu )\left(1+2e^{2}+2e'^{2}\right)+{\frac {3(1-2\mu )\left(1+{\frac {9}{2}}e^{2}+2e'^{2}\right)}{4(1-m)}}\\\\&\quad -{\frac {36+21m-15m^{2}}{4(1-m)}}{\rm {A}}_{1}^{(17)}+{\frac {3(1+m)}{2(1-m)}}{\rm {A}}_{0}^{(18)}e'^{2}\\\\&\quad -{\frac {57-38m}{4(1-m)}}{\rm {A}}_{2}^{(0)}+{\frac {3}{2}}\left({\rm {B}}_{2}^{(14)}+{\rm {B}}_{2}^{(15)}\right){\frac {\gamma ^{2}}{m^{2}}}\end{aligned}}\right\}$

$\times {\frac {a}{a'}}\cos(v-mv)$

$+{\frac {3m^{2}}{4a_{\text{ı}}}}\left\{{\begin{aligned}&{\frac {5(1-2\mu )}{4}}-{\rm {A}}_{0}^{(18)}+{\frac {4+m}{4}}{\rm {A}}_{1}^{(17)}\\\\&\quad -(5+m){\rm {A}}_{1}^{(19)}\end{aligned}}\right\}$

$\times {\frac {a}{a'}}e'\cos(v-mv+c'mv-\varpi ')$

$+{\frac {3m^{2}}{4a_{\text{ı}}(1-2m)}}\left\{{\begin{aligned}&{\frac {15-18m)}{4}}(1-2\mu )-{\frac {76-33m}{4}}{\rm {A}}_{1}^{(17)}\\\\&\quad -5{\rm {A}}_{0}^{(18)}-(1-2m){\rm {A}}_{1}^{(19)}\end{aligned}}\right\}$

$\times {\frac {a}{a'}}e'\cos(v-mv-c'mv+\varpi ')$

Je n’ai point eu égard aux termes multipliés par $\lambda _{2},$ parce qu’ils se détruisent réciproquement, aux quantités près de l’ordre $m^{7}.$