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Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/116
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Ensuite,
b
1
2
(
0
)
=
2,144
440
,
b
1
2
(
1
)
=
0,552
007
,
b
1
2
(
2
)
=
0,208
313
,
b
1
2
(
3
)
=
0,086
834
,
b
1
2
(
4
)
=
0,037
909
,
b
1
2
(
5
)
=
0,016
990
,
b
1
2
(
6
)
=
0,007
728
,
b
1
2
(
7
)
=
0,003
522
,
b
1
2
(
8
)
=
0,001
547
;
d
b
1
2
(
0
)
d
α
=
0,683
055
,
d
b
1
2
(
1
)
d
α
=
1,373
806
,
d
b
1
2
(
2
)
d
α
=
0,949
128
,
d
b
1
2
(
3
)
d
α
=
0,572
896
,
d
b
1
2
(
4
)
d
α
=
0,327
198
,
d
b
1
2
(
5
)
d
α
=
0,181
370
,
d
b
1
2
(
6
)
d
α
=
0,098
799
,
d
b
1
2
(
7
)
d
α
=
0,053
642
;
d
2
b
1
2
(
0
)
d
α
2
=
2,377
102
,
d
2
b
1
2
(
1
)
d
α
2
=
2,017
767
,
d
2
b
1
2
(
2
)
d
α
2
=
2,992
240
,
d
2
b
1
2
(
3
)
d
α
2
=
2,881
218
,
d
2
b
1
2
(
4
)
d
α
2
=
2,278
077
,
d
2
b
1
2
(
5
)
d
α
2
=
1,616
470
,
d
2
b
1
2
(
6
)
d
α
2
=
1,067
430
;
d
3
b
1
2
(
0
)
d
α
3
=
8,798
999
,
d
3
b
1
2
(
1
)
d
α
3
=
9,578
267
,
d
3
b
1
2
(
2
)
d
α
3
=
9,425
450
,
d
3
b
1
2
(
3
)
d
α
3
=
11,904
140
,
d
3
b
1
2
(
4
)
d
α
3
=
12,988
670
,
d
3
b
1
2
(
5
)
d
α
3
=
12,135
721
;
b
3
2
(
0
)
=
3,750
905
,
b
3
2
(
1
)
=
2,547
992
,
b
3
2
(
2
)
=
1,530
452
,
b
3
2
(
3
)
=
0,872
105
,
b
3
2
(
4
)
=
0,482
564
,
b
3
2
(
5
)
=
0,262
146
;
d
b
3
2
(
2
)
d
α
=
9,756
56
,
d
b
3
2
(
3
)
d
α
=
7,240
97
,
d
b
3
2
(
4
)
d
α
=
4,950
52.
{\displaystyle {\begin{alignedat}{3}b_{\frac {1}{2}}^{(0)}&=2{,}144440,\qquad &b_{\frac {1}{2}}^{(1)}&=0{,}552007,\qquad &b_{\frac {1}{2}}^{(2)}&=0{,}208313,\\b_{\frac {1}{2}}^{(3)}&=0{,}086834,&b_{\frac {1}{2}}^{(4)}&=0{,}037909,&b_{\frac {1}{2}}^{(5)}&=0{,}016990,\\b_{\frac {1}{2}}^{(6)}&=0{,}007728,&b_{\frac {1}{2}}^{(7)}&=0{,}003522,&b_{\frac {1}{2}}^{(8)}&=0{,}001547\,;\\\\{\frac {db_{\frac {1}{2}}^{(0)}}{d\alpha }}&=0{,}683055,&{\frac {db_{\frac {1}{2}}^{(1)}}{d\alpha }}&=1{,}373806,&{\frac {db_{\frac {1}{2}}^{(2)}}{d\alpha }}&=0{,}949128,\\{\frac {db_{\frac {1}{2}}^{(3)}}{d\alpha }}&=0{,}572896,&{\frac {db_{\frac {1}{2}}^{(4)}}{d\alpha }}&=0{,}327198,&{\frac {db_{\frac {1}{2}}^{(5)}}{d\alpha }}&=0{,}181370,\\{\frac {db_{\frac {1}{2}}^{(6)}}{d\alpha }}&=0{,}098799,&{\frac {db_{\frac {1}{2}}^{(7)}}{d\alpha }}&=0{,}053642\,;\\\\{\frac {d^{2}b_{\frac {1}{2}}^{(0)}}{d\alpha ^{2}}}&=2{,}377102,&{\frac {d^{2}b_{\frac {1}{2}}^{(1)}}{d\alpha ^{2}}}&=2{,}017767,&{\frac {d^{2}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{2}}}&=2{,}992240,\\{\frac {d^{2}b_{\frac {1}{2}}^{(3)}}{d\alpha ^{2}}}&=2{,}881218,&{\frac {d^{2}b_{\frac {1}{2}}^{(4)}}{d\alpha ^{2}}}&=2{,}278077,&{\frac {d^{2}b_{\frac {1}{2}}^{(5)}}{d\alpha ^{2}}}&=1{,}616470,\\{\frac {d^{2}b_{\frac {1}{2}}^{(6)}}{d\alpha ^{2}}}&=1{,}067430\,;&&&&\\\\{\frac {d^{3}b_{\frac {1}{2}}^{(0)}}{d\alpha ^{3}}}&=\ \,8{,}798999,&{\frac {d^{3}b_{\frac {1}{2}}^{(1)}}{d\alpha ^{3}}}&=\ \,9{,}578267,&{\frac {d^{3}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{3}}}&=\ \,9{,}425450,\\{\frac {d^{3}b_{\frac {1}{2}}^{(3)}}{d\alpha ^{3}}}&=11{,}904140,&{\frac {d^{3}b_{\frac {1}{2}}^{(4)}}{d\alpha ^{3}}}&=12{,}988670,&{\frac {d^{3}b_{\frac {1}{2}}^{(5)}}{d\alpha ^{3}}}&=12{,}135721\,;\\\\b_{\frac {3}{2}}^{(0)}&=3{,}750905,&b_{\frac {3}{2}}^{(1)}&=2{,}547992,&b_{\frac {3}{2}}^{(2)}&=1{,}530452,\\b_{\frac {3}{2}}^{(3)}&=0{,}872105,&b_{\frac {3}{2}}^{(4)}&=0{,}482564,&b_{\frac {3}{2}}^{(5)}&=0{,}262146\,;\\\\{\frac {db_{\frac {3}{2}}^{(2)}}{d\alpha }}&=9{,}75656,&{\frac {db_{\frac {3}{2}}^{(3)}}{d\alpha }}&=7{,}24097,&{\frac {db_{\frac {3}{2}}^{(4)}}{d\alpha }}&=4{,}95052.\end{alignedat}}}
