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Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/113
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d
b
1
2
(
0
)
d
α
=
0,808
789
,
d
b
1
2
(
1
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d
α
=
1,483
154
,
d
b
1
2
(
2
)
d
α
=
1,105
160
,
d
b
1
2
(
3
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d
α
=
0,726
550
,
d
b
1
2
(
4
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d
α
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0,453
285
,
d
b
1
2
(
5
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d
α
=
0,274
717
,
d
b
1
2
(
6
)
d
α
=
0,163
506
,
d
b
1
2
(
7
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d
α
=
0,096
019
,
d
b
1
2
(
8
)
d
α
=
0,056
171
,
d
b
1
2
(
9
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d
α
=
0,033
083
,
d
b
1
2
(
10
)
d
α
=
0,020
265
;
d
2
b
1
2
(
0
)
d
α
2
=
2,875
229
,
d
2
b
1
2
(
1
)
d
α
2
=
2,552
788
,
d
2
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1
2
(
2
)
d
α
2
=
3,521
040
,
d
2
b
1
2
(
3
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d
α
2
=
3,533
622
,
d
2
b
1
2
(
4
)
d
α
2
=
2,995
647
,
d
2
b
1
2
(
5
)
d
α
2
=
2,302
428
,
d
2
b
1
2
(
6
)
d
α
2
=
1,664
586
,
d
2
b
1
2
(
7
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d
α
2
=
1,144
377
,
d
2
b
1
2
(
8
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d
α
2
=
0,760
603
,
d
2
b
1
2
(
9
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d
α
2
=
0,485
135
;
d
3
b
1
2
(
0
)
d
α
3
=
12,128
630
,
d
3
b
1
2
(
1
)
d
α
3
=
12,878
804
,
d
3
b
1
2
(
2
)
d
α
3
=
12,832
050
,
d
3
b
1
2
(
3
)
d
α
3
=
15,454
850
,
d
3
b
1
2
(
4
)
d
α
3
=
17,058
155
,
d
3
b
1
2
(
5
)
d
α
3
=
16,655
445
,
d
3
b
1
2
(
6
)
d
α
3
=
14,958
762
,
d
3
b
1
2
(
7
)
d
α
3
=
12,234
874
,
d
3
b
1
2
(
8
)
d
α
3
=
9,566
420
;
d
4
b
1
2
(
0
)
d
α
4
=
84,401
59
,
d
4
b
1
2
(
1
)
d
α
4
=
83,948
25
,
d
4
b
1
2
(
2
)
d
α
4
=
87,302
7
,
d
4
b
1
2
(
3
)
d
α
4
=
89,861
5
,
d
4
b
1
2
(
4
)
d
α
4
=
101,380
9
,
d
4
b
1
2
(
5
)
d
α
4
=
113,522
8
,
d
4
b
1
2
(
6
)
d
α
4
=
118,660
7
,
d
4
b
1
2
(
7
)
d
α
4
=
115,958
8
;
{\displaystyle {\begin{alignedat}{3}{\frac {db_{\frac {1}{2}}^{(0)}}{d\alpha }}&=0{,}808789,&\qquad {\frac {db_{\frac {1}{2}}^{(1)}}{d\alpha }}&=1{,}483154,&\qquad {\frac {db_{\frac {1}{2}}^{(2)}}{d\alpha }}&=1{,}105160,\\{\frac {db_{\frac {1}{2}}^{(3)}}{d\alpha }}&=0{,}726550,&{\frac {db_{\frac {1}{2}}^{(4)}}{d\alpha }}&=0{,}453285,&{\frac {db_{\frac {1}{2}}^{(5)}}{d\alpha }}&=0{,}274717,\\{\frac {db_{\frac {1}{2}}^{(6)}}{d\alpha }}&=0{,}163506,&{\frac {db_{\frac {1}{2}}^{(7)}}{d\alpha }}&=0{,}096019,&{\frac {db_{\frac {1}{2}}^{(8)}}{d\alpha }}&=0{,}056171,\\{\frac {db_{\frac {1}{2}}^{(9)}}{d\alpha }}&=0{,}033083,&{\frac {db_{\frac {1}{2}}^{(10)}}{d\alpha }}&=0{,}020265\,;\\\\{\frac {d^{2}b_{\frac {1}{2}}^{(0)}}{d\alpha ^{2}}}&=2{,}875229,&{\frac {d^{2}b_{\frac {1}{2}}^{(1)}}{d\alpha ^{2}}}&=2{,}552788,&{\frac {d^{2}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{2}}}&=3{,}521040,\\{\frac {d^{2}b_{\frac {1}{2}}^{(3)}}{d\alpha ^{2}}}&=3{,}533622,&{\frac {d^{2}b_{\frac {1}{2}}^{(4)}}{d\alpha ^{2}}}&=2{,}995647,&{\frac {d^{2}b_{\frac {1}{2}}^{(5)}}{d\alpha ^{2}}}&=2{,}302428,\\{\frac {d^{2}b_{\frac {1}{2}}^{(6)}}{d\alpha ^{2}}}&=1{,}664586,&{\frac {d^{2}b_{\frac {1}{2}}^{(7)}}{d\alpha ^{2}}}&=1{,}144377,&{\frac {d^{2}b_{\frac {1}{2}}^{(8)}}{d\alpha ^{2}}}&=0{,}760603,\\{\frac {d^{2}b_{\frac {1}{2}}^{(9)}}{d\alpha ^{2}}}&=0{,}485135\,;\\\\{\frac {d^{3}b_{\frac {1}{2}}^{(0)}}{d\alpha ^{3}}}&=12{,}128630,&{\frac {d^{3}b_{\frac {1}{2}}^{(1)}}{d\alpha ^{3}}}&=12{,}878804,&{\frac {d^{3}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{3}}}&=12{,}832050,\\{\frac {d^{3}b_{\frac {1}{2}}^{(3)}}{d\alpha ^{3}}}&=15{,}454850,&{\frac {d^{3}b_{\frac {1}{2}}^{(4)}}{d\alpha ^{3}}}&=17{,}058155,&{\frac {d^{3}b_{\frac {1}{2}}^{(5)}}{d\alpha ^{3}}}&=16{,}655445,\\{\frac {d^{3}b_{\frac {1}{2}}^{(6)}}{d\alpha ^{3}}}&=14{,}958762,&{\frac {d^{3}b_{\frac {1}{2}}^{(7)}}{d\alpha ^{3}}}&=12{,}234874,&{\frac {d^{3}b_{\frac {1}{2}}^{(8)}}{d\alpha ^{3}}}&=\,\ 9{,}566420\,;\\\\{\frac {d^{4}b_{\frac {1}{2}}^{(0)}}{d\alpha ^{4}}}&=\,\ 84{,}40159,&{\frac {d^{4}b_{\frac {1}{2}}^{(1)}}{d\alpha ^{4}}}&=\,\ 83{,}94825,&{\frac {d^{4}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{4}}}&=\,\ 87{,}3027,\\{\frac {d^{4}b_{\frac {1}{2}}^{(3)}}{d\alpha ^{4}}}&=\,\ 89{,}8615,&{\frac {d^{4}b_{\frac {1}{2}}^{(4)}}{d\alpha ^{4}}}&=101{,}3809,&{\frac {d^{4}b_{\frac {1}{2}}^{(5)}}{d\alpha ^{4}}}&=113{,}5228,\\{\frac {d^{4}b_{\frac {1}{2}}^{(6)}}{d\alpha ^{4}}}&=118{,}6607,&{\frac {d^{4}b_{\frac {1}{2}}^{(7)}}{d\alpha ^{4}}}&=115{,}9588\,;\end{alignedat}}}