Page:Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/104

vénus et mars.

$\alpha ={\frac {a'}{a'''}}=0{,}47472320,$

d’où l’on a conclu

${\begin{aligned}b_{-{\frac {1}{2}}}^{(0)}&=2{,}11436649,\\b_{-{\frac {1}{2}}}^{(1)}&=-0{,}46094390.\end{aligned}}$

Ensuite,

${\begin{alignedat}{3}b_{\frac {1}{2}}^{(0)}&=2{,}129668,\qquad &b_{\frac {1}{2}}^{(1)}&=0{,}521624,\qquad &b_{\frac {1}{2}}^{(2)}&=0{,}187726,\\b_{\frac {1}{2}}^{(3)}&=0{,}074675,&b_{\frac {1}{2}}^{(4)}&=0{,}031127,&b_{\frac {1}{2}}^{(5)}&=0{,}013337,\\b_{\frac {1}{2}}^{(6)}&=0{,}005829\,;&&&&\\\\{\frac {db_{\frac {1}{2}}^{(0)}}{d\alpha }}&=0{,}631752,&{\frac {db_{\frac {1}{2}}^{(1)}}{d\alpha }}&=1{,}330781,&{\frac {db_{\frac {1}{2}}^{(2)}}{d\alpha }}&=0{,}884106,\\{\frac {db_{\frac {1}{2}}^{(3)}}{d\alpha }}&=0{,}510976,&{\frac {db_{\frac {1}{2}}^{(4)}}{d\alpha }}&=0{,}279002,&{\frac {db_{\frac {1}{2}}^{(5)}}{d\alpha }}&=0{,}147606\,;\\\\{\frac {d^{2}b_{\frac {1}{2}}^{(0)}}{d\alpha ^{2}}}&=2{,}192778,&{\frac {d^{2}b_{\frac {1}{2}}^{(1)}}{d\alpha ^{2}}}&=1{,}815836,&{\frac {d^{2}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{2}}}&=2{,}795574,\\{\frac {d^{2}b_{\frac {1}{2}}^{(3)}}{d\alpha ^{2}}}&=2{,}628516,&{\frac {d^{2}b_{\frac {1}{2}}^{(4)}}{d\alpha ^{2}}}&=2{,}004429\,;&&\\\\{\frac {d^{3}b_{\frac {1}{2}}^{(0)}}{d\alpha ^{3}}}&=7{,}65440,&{\frac {d^{3}b_{\frac {1}{2}}^{(1)}}{d\alpha ^{3}}}&=8{,}45655,&{\frac {d^{3}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{3}}}&=8{,}17676,\\{\frac {d^{3}b_{\frac {1}{2}}^{(3)}}{d\alpha ^{3}}}&=10{,}66513\,;&&&&\\\\b_{\frac {3}{2}}^{(0)}&=3{,}523572,&b_{\frac {3}{2}}^{(1)}&=2{,}304481,&b_{\frac {3}{2}}^{(2)}&=1{,}325959,\\b_{\frac {3}{2}}^{(3)}&=0{,}722687\,;&&&&\\\\&&{\frac {db_{\frac {3}{2}}^{(2)}}{d\alpha }}&=8{,}47521.\end{alignedat}}$