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Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/114
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d
5
b
1
2
(
0
)
d
α
5
=
747,480
,
d
5
b
1
2
(
1
)
d
α
5
=
753,417
,
d
5
b
1
2
(
2
)
d
α
5
=
761,843
,
d
5
b
1
2
(
3
)
d
α
5
=
785,884
,
d
5
b
1
2
(
4
)
d
α
5
=
819,180
,
d
5
b
1
2
(
5
)
d
α
5
=
884,505
,
d
5
b
1
2
(
6
)
d
α
5
=
912,301
;
b
3
2
(
0
)
=
4,358
387
,
b
3
2
(
1
)
=
3,185
493
,
b
3
2
(
2
)
=
2,082
131
,
b
3
2
(
3
)
=
1,295
672
,
b
3
2
(
4
)
=
0,784
084
,
b
3
2
(
5
)
=
0,466
047
,
b
3
2
(
6
)
=
0,273
629
,
b
3
2
(
7
)
=
0,158
799
,
b
3
2
(
8
)
=
0,092
290
,
b
3
2
(
9
)
=
0,053
922
;
d
b
3
2
(
0
)
d
α
=
14,681
324
,
d
b
3
2
(
1
)
d
α
=
15,239
657
,
d
b
3
2
(
2
)
d
α
=
13,416
026
,
d
b
3
2
(
3
)
d
α
=
10,598
611
,
d
b
3
2
(
4
)
d
α
=
7,802
247
,
d
b
3
2
(
5
)
d
α
=
5,470
398
,
d
b
3
2
(
6
)
d
α
=
3,710
043
,
d
b
3
2
(
7
)
d
α
=
2,426
079
,
d
b
3
2
(
8
)
d
α
=
1,563
695
;
d
2
b
3
2
(
0
)
d
α
2
=
96,685
36
,
d
2
b
3
2
(
1
)
d
α
2
=
94,917
01
,
d
2
b
3
2
(
2
)
d
α
2
=
93,192
82
,
d
2
b
3
2
(
3
)
d
α
2
=
86,902
15
,
d
2
b
3
2
(
4
)
d
α
2
=
75,081
15
,
d
2
b
3
2
(
5
)
d
α
2
=
61,101
55
,
d
2
b
3
2
(
6
)
d
α
2
=
47,481
85
,
d
2
b
3
2
(
7
)
d
α
2
=
35,743
55
;
d
3
b
3
2
(
0
)
d
α
3
=
830,058
6
,
d
3
b
3
2
(
1
)
d
α
3
=
830,158
0
,
d
3
b
3
2
(
2
)
d
α
3
=
810,104
5
,
d
3
b
3
2
(
3
)
d
α
3
=
785,585
5
,
d
3
b
3
2
(
4
)
d
α
3
=
740,677
5
,
d
3
b
3
2
(
5
)
d
α
3
=
666,408
0
,
d
3
b
3
2
(
6
)
d
α
3
=
574,911
5.
{\displaystyle {\begin{alignedat}{3}{\frac {d^{5}b_{\frac {1}{2}}^{(0)}}{d\alpha ^{5}}}&=747{,}480,&\qquad {\frac {d^{5}b_{\frac {1}{2}}^{(1)}}{d\alpha ^{5}}}&=753{,}417,&\qquad {\frac {d^{5}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{5}}}&=761{,}843,\\{\frac {d^{5}b_{\frac {1}{2}}^{(3)}}{d\alpha ^{5}}}&=785{,}884,&{\frac {d^{5}b_{\frac {1}{2}}^{(4)}}{d\alpha ^{5}}}&=819{,}180,&{\frac {d^{5}b_{\frac {1}{2}}^{(5)}}{d\alpha ^{5}}}&=884{,}505,\\{\frac {d^{5}b_{\frac {1}{2}}^{(6)}}{d\alpha ^{5}}}&=912{,}301\,;\\\\b_{\frac {3}{2}}^{(0)}&=4{,}358387,&b_{\frac {3}{2}}^{(1)}&=3{,}185493,&b_{\frac {3}{2}}^{(2)}&=2{,}082131,\\b_{\frac {3}{2}}^{(3)}&=1{,}295672,&b_{\frac {3}{2}}^{(4)}&=0{,}784084,&b_{\frac {3}{2}}^{(5)}&=0{,}466047,\\b_{\frac {3}{2}}^{(6)}&=0{,}273629,&b_{\frac {3}{2}}^{(7)}&=0{,}158799,&b_{\frac {3}{2}}^{(8)}&=0{,}092290,\\b_{\frac {3}{2}}^{(9)}&=0{,}053922\,;\\\\{\frac {db_{\frac {3}{2}}^{(0)}}{d\alpha }}&=14{,}681324,&{\frac {db_{\frac {3}{2}}^{(1)}}{d\alpha }}&=15{,}239657,&{\frac {db_{\frac {3}{2}}^{(2)}}{d\alpha }}&=13{,}416026,\\{\frac {db_{\frac {3}{2}}^{(3)}}{d\alpha }}&=10{,}598611,&{\frac {db_{\frac {3}{2}}^{(4)}}{d\alpha }}&=\,\ 7{,}802247,&{\frac {db_{\frac {3}{2}}^{(5)}}{d\alpha }}&=\,\ 5{,}470398,\\{\frac {db_{\frac {3}{2}}^{(6)}}{d\alpha }}&=\,\ 3{,}710043,&{\frac {db_{\frac {3}{2}}^{(7)}}{d\alpha }}&=\,\ 2{,}426079,&{\frac {db_{\frac {3}{2}}^{(8)}}{d\alpha }}&=\,\ 1{,}563695\,;\\\\{\frac {d^{2}b_{\frac {3}{2}}^{(0)}}{d\alpha ^{2}}}&=96{,}68536,&{\frac {d^{2}b_{\frac {3}{2}}^{(1)}}{d\alpha ^{2}}}&=94{,}91701,&{\frac {d^{2}b_{\frac {3}{2}}^{(2)}}{d\alpha ^{2}}}&=93{,}19282,\\{\frac {d^{2}b_{\frac {3}{2}}^{(3)}}{d\alpha ^{2}}}&=86{,}90215,&{\frac {d^{2}b_{\frac {3}{2}}^{(4)}}{d\alpha ^{2}}}&=75{,}08115,&{\frac {d^{2}b_{\frac {3}{2}}^{(5)}}{d\alpha ^{2}}}&=61{,}10155,\\{\frac {d^{2}b_{\frac {3}{2}}^{(6)}}{d\alpha ^{2}}}&=47{,}48185,&{\frac {d^{2}b_{\frac {3}{2}}^{(7)}}{d\alpha ^{2}}}&=35{,}74355\,;\\\\{\frac {d^{3}b_{\frac {3}{2}}^{(0)}}{d\alpha ^{3}}}&=830{,}0586,&{\frac {d^{3}b_{\frac {3}{2}}^{(1)}}{d\alpha ^{3}}}&=830{,}1580,&{\frac {d^{3}b_{\frac {3}{2}}^{(2)}}{d\alpha ^{3}}}&=810{,}1045,\\{\frac {d^{3}b_{\frac {3}{2}}^{(3)}}{d\alpha ^{3}}}&=785{,}5855,&{\frac {d^{3}b_{\frac {3}{2}}^{(4)}}{d\alpha ^{3}}}&=740{,}6775,&{\frac {d^{3}b_{\frac {3}{2}}^{(5)}}{d\alpha ^{3}}}&=666{,}4080,\\{\frac {d^{3}b_{\frac {3}{2}}^{(6)}}{d\alpha ^{3}}}&=574{,}9115.\end{alignedat}}}
