Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/111

${\begin{alignedat}{3}b_{\frac {3}{2}}^{(0)}&=2{,}444762,&b_{\frac {3}{2}}^{(1)}&=1{,}040206,&b_{\frac {3}{2}}^{(2)}&=0{,}376693,\\b_{\frac {3}{2}}^{(3)}&=0{,}127942\,;\\\\{\frac {db_{\frac {3}{2}}^{(0)}}{d\alpha }}&=3{,}48815,&{\frac {db_{\frac {3}{2}}^{(1)}}{d\alpha }}&=4{,}80540,&{\frac {db_{\frac {3}{2}}^{(2)}}{d\alpha }}&=2{,}99684.\end{alignedat}}$

mars et saturne.

$\alpha ={\frac {a'''}{a^{\rm {v}}}}=0{,}15975187,$

d’où l’on a conclu

${\begin{aligned}b_{-{\frac {1}{2}}}^{(0)}&=2{,}01278081,\\b_{-{\frac {1}{2}}}^{(1)}&=-0{,}15924060.\end{aligned}}$

Ensuite,

${\begin{alignedat}{3}b_{\frac {1}{2}}^{(0)}&=2{,}012945,\qquad &b_{\frac {1}{2}}^{(1)}&=0{,}161305,\qquad &b_{\frac {1}{2}}^{(2)}&=0{,}019347,\\b_{\frac {1}{2}}^{(3)}&=0{,}002577,&b_{\frac {1}{2}}^{(4)}&=0{,}000360,&b_{\frac {1}{2}}^{(5)}&=0{,}000052\,;\\\\{\frac {db_{\frac {1}{2}}^{(0)}}{d\alpha }}&=0{,}164463,&{\frac {db_{\frac {1}{2}}^{(1)}}{d\alpha }}&=1{,}029493,&{\frac {db_{\frac {1}{2}}^{(2)}}{d\alpha }}&=0{,}244843,\\{\frac {db_{\frac {1}{2}}^{(3)}}{d\alpha }}&=0{,}048740,&{\frac {db_{\frac {1}{2}}^{(4)}}{d\alpha }}&=0{,}009065\,;\\\\{\frac {d^{2}b_{\frac {1}{2}}^{(0)}}{d\alpha ^{2}}}&=1{,}090095,&{\frac {d^{2}b_{\frac {1}{2}}^{(1)}}{d\alpha ^{2}}}&=0{,}379322,&{\frac {d^{2}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{2}}}&=1{,}596248,\\{\frac {d^{2}b_{\frac {1}{2}}^{(3)}}{d\alpha ^{2}}}&=0{,}620632\,;\\\\b_{\frac {3}{2}}^{(0)}&=2{,}119585,&b_{\frac {3}{2}}^{(1)}&=0{,}503071,&b_{\frac {3}{2}}^{(2)}&=0{,}100136.\end{alignedat}}$