Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/99

Ensuite,

${\begin{alignedat}{3}b_{\frac {1}{2}}^{(0)}&=2{,}081980,\qquad &b_{\frac {1}{2}}^{(1)}&=0{,}411140,\qquad &b_{\frac {1}{2}}^{(2)}&=0{,}120178,\\b_{\frac {1}{2}}^{(3)}&=0{,}038900,&b_{\frac {1}{2}}^{(4)}&=0{,}013202,&b_{\frac {1}{2}}^{(5)}&=0{,}004603,\\b_{\frac {1}{2}}^{(6)}&=0{,}001629,&b_{\frac {1}{2}}^{(7)}&=0{,}000573,&b_{\frac {1}{2}}^{(8)}&=0{,}000177\,;\\\\{\frac {db_{\frac {1}{2}}^{(0)}}{d\alpha }}&=0{,}464378,&{\frac {db_{\frac {1}{2}}^{(1)}}{d\alpha }}&=1{,}199633,&{\frac {db_{\frac {1}{2}}^{(2)}}{d\alpha }}&=0{,}665739,\\{\frac {db_{\frac {1}{2}}^{(3)}}{d\alpha }}&=0{,}316756,&{\frac {db_{\frac {1}{2}}^{(4)}}{d\alpha }}&=0{,}141792,&{\frac {db_{\frac {1}{2}}^{(5)}}{d\alpha }}&=0{,}061433,\\{\frac {db_{\frac {1}{2}}^{(6)}}{d\alpha }}&=0{,}026130,&{\frac {db_{\frac {1}{2}}^{(7)}}{d\alpha }}&=0{,}011153,\\\\{\frac {d^{2}b_{\frac {1}{2}}^{(0)}}{d\alpha ^{2}}}&=1{,}672199,&{\frac {d^{2}b_{\frac {1}{2}}^{(1)}}{d\alpha ^{2}}}&=1{,}220775,&{\frac {d^{2}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{2}}}&=2{,}235935,\\{\frac {d^{2}b_{\frac {1}{2}}^{(3)}}{d\alpha ^{2}}}&=1{,}852364,&{\frac {d^{2}b_{\frac {1}{2}}^{(4)}}{d\alpha ^{2}}}&=1{,}197245,&{\frac {d^{2}b_{\frac {1}{2}}^{(5)}}{d\alpha ^{2}}}&=0{,}670874\,;\\\\{\frac {d^{3}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{3}}}&=5{,}49232,&{\frac {d^{3}b_{\frac {1}{2}}^{(3)}}{d\alpha ^{3}}}&=5{,}45663,&{\frac {d^{3}b_{\frac {1}{2}}^{(4)}}{d\alpha ^{3}}}&=6{,}51373\,;\\\\b_{\frac {3}{2}}^{(0)}&=2{,}871833,&b_{\frac {3}{2}}^{(1)}&=1{,}576062,&b_{\frac {3}{2}}^{(2)}&=0{,}747619,\\b_{\frac {3}{2}}^{(3)}&=0{,}334212,&b_{\frac {3}{2}}^{(4)}&=0{,}153779\,;&\\\\&&{\frac {db_{\frac {3}{2}}^{(3)}}{d\alpha }}&=3{,}05535.&\end{alignedat}}$

mercure et mars.

$\alpha ={\frac {a}{a'''}}=0{,}25405312,$

d’où l’on a conclu

${\begin{aligned}b_{-{\frac {1}{2}}}^{(0)}=&\quad 2{,}03240384.,\\b_{-{\frac {1}{2}}}^{(1)}=&-0{,}25198657.\end{aligned}}$