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Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/110
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mars et jupiter.
α
=
a
‴
a
i
v
=
0,292
90212
,
{\displaystyle \alpha ={\frac {a'''}{a^{\rm {iv}}}}=0{,}29290212,}
d’où l’on a conclu
b
−
1
2
(
0
)
=
2,043
4576
,
b
−
1
2
(
1
)
=
−
0,289
77479.
{\displaystyle {\begin{aligned}b_{-{\frac {1}{2}}}^{(0)}&=2{,}0434576,\\b_{-{\frac {1}{2}}}^{(1)}&=-0{,}28977479.\end{aligned}}}
Ensuite,
b
1
2
(
0
)
=
2,045
112
,
b
1
2
(
1
)
=
0,302
922
,
b
1
2
(
2
)
=
0,066
812
,
b
1
2
(
3
)
=
0,016
357
,
b
1
2
(
4
)
=
0,004
192
,
b
1
2
(
5
)
=
0,001
109
,
b
1
2
(
6
)
=
0,000
297
,
b
1
2
(
7
)
=
0,000
081
;
d
b
1
2
(
0
)
d
α
=
0,324
004
,
d
b
1
2
(
1
)
d
α
=
1,105
998
,
d
b
1
2
(
2
)
d
α
=
0,473
717
,
d
b
1
2
(
3
)
d
α
=
0,172
096
,
d
b
1
2
(
4
)
d
α
=
0,058
420
,
d
b
1
2
(
5
)
d
α
=
0,019
258
,
d
b
1
2
(
6
)
d
α
=
0,006
173
;
d
2
b
1
2
(
0
)
d
α
2
=
1,338
759
,
d
2
b
1
2
(
1
)
d
α
2
=
0,794
557
,
d
2
b
1
2
(
2
)
d
α
2
=
1,871
538
,
d
2
b
1
2
(
3
)
d
α
2
=
1,258
858
,
d
2
b
1
2
(
4
)
d
α
2
=
0,623
184
;
d
3
b
1
2
(
0
)
d
α
3
=
2,693
58
,
d
3
b
1
2
(
1
)
d
α
3
=
3,777
22
,
d
3
b
1
2
(
2
)
d
α
3
=
2,910
68
,
d
3
b
1
2
(
3
)
d
α
3
=
5,470
68
;
{\displaystyle {\begin{alignedat}{3}b_{\frac {1}{2}}^{(0)}&=2{,}045112,\qquad &b_{\frac {1}{2}}^{(1)}&=0{,}302922,\qquad &b_{\frac {1}{2}}^{(2)}&=0{,}066812,\\b_{\frac {1}{2}}^{(3)}&=0{,}016357,&b_{\frac {1}{2}}^{(4)}&=0{,}004192,&b_{\frac {1}{2}}^{(5)}&=0{,}001109,\\b_{\frac {1}{2}}^{(6)}&=0{,}000297,&b_{\frac {1}{2}}^{(7)}&=0{,}000081\,;\\\\{\frac {db_{\frac {1}{2}}^{(0)}}{d\alpha }}&=0{,}324004,&{\frac {db_{\frac {1}{2}}^{(1)}}{d\alpha }}&=1{,}105998,&{\frac {db_{\frac {1}{2}}^{(2)}}{d\alpha }}&=0{,}473717,\\{\frac {db_{\frac {1}{2}}^{(3)}}{d\alpha }}&=0{,}172096,&{\frac {db_{\frac {1}{2}}^{(4)}}{d\alpha }}&=0{,}058420,&{\frac {db_{\frac {1}{2}}^{(5)}}{d\alpha }}&=0{,}019258,\\{\frac {db_{\frac {1}{2}}^{(6)}}{d\alpha }}&=0{,}006173\,;\\\\{\frac {d^{2}b_{\frac {1}{2}}^{(0)}}{d\alpha ^{2}}}&=1{,}338759,&{\frac {d^{2}b_{\frac {1}{2}}^{(1)}}{d\alpha ^{2}}}&=0{,}794557,&{\frac {d^{2}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{2}}}&=1{,}871538,\\{\frac {d^{2}b_{\frac {1}{2}}^{(3)}}{d\alpha ^{2}}}&=1{,}258858,&{\frac {d^{2}b_{\frac {1}{2}}^{(4)}}{d\alpha ^{2}}}&=0{,}623184\,;\\\\{\frac {d^{3}b_{\frac {1}{2}}^{(0)}}{d\alpha ^{3}}}&=2{,}69358,&{\frac {d^{3}b_{\frac {1}{2}}^{(1)}}{d\alpha ^{3}}}&=3{,}77722,&{\frac {d^{3}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{3}}}&=2{,}91068,\\{\frac {d^{3}b_{\frac {1}{2}}^{(3)}}{d\alpha ^{3}}}&=5{,}47068\,;\end{alignedat}}}