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Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/107
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b
1
2
(
0
)
=
2,291
182
,
b
1
2
(
1
)
=
0,804
563
,
b
1
2
(
2
)
=
0,405
584
,
b
1
2
(
3
)
=
0,224
598
,
b
1
2
(
4
)
=
0,129
973
,
b
1
2
(
5
)
=
0,077
170
,
b
1
2
(
6
)
=
0,046
595
,
b
1
2
(
7
)
=
0,028
480
,
b
1
2
(
8
)
=
0,017
565
;
d
b
1
2
(
0
)
d
α
=
1,228
078
,
d
b
1
2
(
1
)
d
α
=
1,871
211
,
d
b
1
2
(
2
)
d
α
=
1,601
236
,
d
b
1
2
(
3
)
d
α
=
1,240
990
,
d
b
1
2
(
4
)
d
α
=
0,920
710
,
d
b
1
2
(
5
)
d
α
=
0,666
207
,
d
b
1
2
(
6
)
d
α
=
0,473
942
,
d
b
1
2
(
7
)
d
α
=
0,333
444
;
d
2
b
1
2
(
0
)
d
α
2
=
4,985
108
,
d
2
b
1
2
(
1
)
d
α
2
=
4,744
671
,
d
2
b
1
2
(
2
)
d
α
2
=
5,731
111
,
d
2
b
1
2
(
3
)
d
α
2
=
6,057
860
,
d
2
b
1
2
(
4
)
d
α
2
=
5,776
483
,
d
2
b
1
2
(
5
)
d
α
2
=
5,141
993
,
d
2
b
1
2
(
6
)
d
α
2
=
4,388
001
;
d
3
b
1
2
(
0
)
d
α
3
=
29,034
00
,
d
3
b
1
2
(
1
)
d
α
3
=
29,789
30
,
d
3
b
1
2
(
2
)
d
α
3
=
30,188
48
,
d
3
b
1
2
(
3
)
d
α
3
=
33,293
81
,
d
3
b
1
2
(
4
)
d
α
3
=
36,320
93
,
d
3
b
1
2
(
5
)
d
α
3
=
37,239
08
;
b
3
2
(
0
)
=
6,856
336
,
b
3
2
(
1
)
=
5,727
893
,
b
3
2
(
2
)
=
4,404
530
,
b
3
2
(
3
)
=
3,255
964
,
b
3
2
(
4
)
=
2,351
254
,
b
3
2
(
5
)
=
1,671
668
,
b
3
2
(
6
)
=
1,174
650
;
d
b
3
2
(
2
)
d
α
=
31,808
97
,
d
b
3
2
(
3
)
d
α
=
32,262
85
,
d
b
3
2
(
5
)
d
α
=
18,258
67.
{\displaystyle {\begin{alignedat}{3}b_{\frac {1}{2}}^{(0)}&=2{,}291182,\qquad &b_{\frac {1}{2}}^{(1)}&=0{,}804563,\qquad &b_{\frac {1}{2}}^{(2)}&=0{,}405584,\\b_{\frac {1}{2}}^{(3)}&=0{,}224598,&b_{\frac {1}{2}}^{(4)}&=0{,}129973,&b_{\frac {1}{2}}^{(5)}&=0{,}077170,\\b_{\frac {1}{2}}^{(6)}&=0{,}046595,&b_{\frac {1}{2}}^{(7)}&=0{,}028480,&b_{\frac {1}{2}}^{(8)}&=0{,}017565\,;\\\\{\frac {db_{\frac {1}{2}}^{(0)}}{d\alpha }}&=1{,}228078,&{\frac {db_{\frac {1}{2}}^{(1)}}{d\alpha }}&=1{,}871211,&{\frac {db_{\frac {1}{2}}^{(2)}}{d\alpha }}&=1{,}601236,\\{\frac {db_{\frac {1}{2}}^{(3)}}{d\alpha }}&=1{,}240990,&{\frac {db_{\frac {1}{2}}^{(4)}}{d\alpha }}&=0{,}920710,&{\frac {db_{\frac {1}{2}}^{(5)}}{d\alpha }}&=0{,}666207,\\{\frac {db_{\frac {1}{2}}^{(6)}}{d\alpha }}&=0{,}473942,&{\frac {db_{\frac {1}{2}}^{(7)}}{d\alpha }}&=0{,}333444\,;\\\\{\frac {d^{2}b_{\frac {1}{2}}^{(0)}}{d\alpha ^{2}}}&=4{,}985108,&{\frac {d^{2}b_{\frac {1}{2}}^{(1)}}{d\alpha ^{2}}}&=4{,}744671,&{\frac {d^{2}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{2}}}&=5{,}731111,\\{\frac {d^{2}b_{\frac {1}{2}}^{(3)}}{d\alpha ^{2}}}&=6{,}057860,&{\frac {d^{2}b_{\frac {1}{2}}^{(4)}}{d\alpha ^{2}}}&=5{,}776483,&{\frac {d^{2}b_{\frac {1}{2}}^{(5)}}{d\alpha ^{2}}}&=5{,}141993,\\{\frac {d^{2}b_{\frac {1}{2}}^{(6)}}{d\alpha ^{2}}}&=4{,}388001\,;&&&&\\\\{\frac {d^{3}b_{\frac {1}{2}}^{(0)}}{d\alpha ^{3}}}&=29{,}03400,&{\frac {d^{3}b_{\frac {1}{2}}^{(1)}}{d\alpha ^{3}}}&=29{,}78930,&{\frac {d^{3}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{3}}}&=30{,}18848,\\{\frac {d^{3}b_{\frac {1}{2}}^{(3)}}{d\alpha ^{3}}}&=33{,}29381,&{\frac {d^{3}b_{\frac {1}{2}}^{(4)}}{d\alpha ^{3}}}&=36{,}32093,&{\frac {d^{3}b_{\frac {1}{2}}^{(5)}}{d\alpha ^{3}}}&=37{,}23908\,;\\\\b_{\frac {3}{2}}^{(0)}&=6{,}856336,&b_{\frac {3}{2}}^{(1)}&=5{,}727893,&b_{\frac {3}{2}}^{(2)}&=4{,}404530,\\b_{\frac {3}{2}}^{(3)}&=3{,}255964,&b_{\frac {3}{2}}^{(4)}&=2{,}351254,&b_{\frac {3}{2}}^{(5)}&=1{,}671668,\\b_{\frac {3}{2}}^{(6)}&=1{,}174650\,;\\\\{\frac {db_{\frac {3}{2}}^{(2)}}{d\alpha }}&=31{,}80897,&{\frac {db_{\frac {3}{2}}^{(3)}}{d\alpha }}&=32{,}26285,&{\frac {db_{\frac {3}{2}}^{(5)}}{d\alpha }}&=18{,}25867.\end{alignedat}}}