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Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/103
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Ensuite,
b
1
2
(
0
)
=
2,386
343
,
b
1
2
(
1
)
=
0,942
413
,
b
1
2
(
2
)
=
0,527
589
,
b
1
2
(
3
)
=
0,323
359
,
b
1
2
(
4
)
=
0,206
811
,
b
1
2
(
5
)
=
0,135
616
,
b
1
2
(
6
)
=
0,090
412
,
b
1
2
(
7
)
=
0,061
101
,
b
1
2
(
8
)
=
0,041
731
;
d
b
1
2
(
0
)
d
α
=
1,643
709
,
d
b
1
2
(
1
)
d
α
=
2,272
414
,
d
b
1
2
(
2
)
d
α
=
2,069
770
,
d
b
1
2
(
3
)
d
α
=
1,738
781
,
d
b
1
2
(
4
)
d
α
=
1,407
491
,
d
b
1
2
(
5
)
d
α
=
1,113
704
,
d
b
1
2
(
6
)
d
α
=
0,867
147
,
d
b
1
2
(
7
)
d
α
=
0,668
830
;
d
2
b
1
2
(
0
)
d
α
2
=
7,719
923
,
d
2
b
1
2
(
1
)
d
α
2
=
7,531
096
,
d
2
b
1
2
(
2
)
d
α
2
=
8,558
595
,
d
2
b
1
2
(
3
)
d
α
2
=
9,112
527
,
d
2
b
1
2
(
4
)
d
α
2
=
9,107
400
,
d
2
b
1
2
(
5
)
d
α
2
=
8,634
030
,
d
2
b
1
2
(
6
)
d
α
2
=
7,842
733
;
d
3
b
1
2
(
0
)
d
α
3
=
56,553
35
,
d
3
b
1
2
(
1
)
d
α
3
=
57,357
21
,
d
3
b
1
2
(
2
)
d
α
3
=
58,196
33
,
d
3
b
1
2
(
3
)
d
α
3
=
62,876
46
,
d
3
b
1
2
(
4
)
d
α
3
=
66,324
09
,
d
3
b
1
2
(
5
)
d
α
3
=
70,543
26
;
b
3
2
(
0
)
=
9,992
539
,
b
3
2
(
1
)
=
8,871
894
,
b
3
2
(
2
)
=
7,386
580
,
b
3
2
(
3
)
=
5,953
940
,
b
3
2
(
4
)
=
4,704
321
,
b
3
2
(
5
)
=
3,652
052
;
{\displaystyle {\begin{alignedat}{3}b_{\frac {1}{2}}^{(0)}&=2{,}386343,\qquad &b_{\frac {1}{2}}^{(1)}&=0{,}942413,\qquad &b_{\frac {1}{2}}^{(2)}&=0{,}527589,\\b_{\frac {1}{2}}^{(3)}&=0{,}323359,&b_{\frac {1}{2}}^{(4)}&=0{,}206811,&b_{\frac {1}{2}}^{(5)}&=0{,}135616,\\b_{\frac {1}{2}}^{(6)}&=0{,}090412,&b_{\frac {1}{2}}^{(7)}&=0{,}061101,&b_{\frac {1}{2}}^{(8)}&=0{,}041731\,;\\\\{\frac {db_{\frac {1}{2}}^{(0)}}{d\alpha }}&=1{,}643709,&{\frac {db_{\frac {1}{2}}^{(1)}}{d\alpha }}&=2{,}272414,&{\frac {db_{\frac {1}{2}}^{(2)}}{d\alpha }}&=2{,}069770,\\{\frac {db_{\frac {1}{2}}^{(3)}}{d\alpha }}&=1{,}738781,&{\frac {db_{\frac {1}{2}}^{(4)}}{d\alpha }}&=1{,}407491,&{\frac {db_{\frac {1}{2}}^{(5)}}{d\alpha }}&=1{,}113704,\\{\frac {db_{\frac {1}{2}}^{(6)}}{d\alpha }}&=0{,}867147,&{\frac {db_{\frac {1}{2}}^{(7)}}{d\alpha }}&=0{,}668830\,;\\\\{\frac {d^{2}b_{\frac {1}{2}}^{(0)}}{d\alpha ^{2}}}&=7{,}719923,&{\frac {d^{2}b_{\frac {1}{2}}^{(1)}}{d\alpha ^{2}}}&=7{,}531096,&{\frac {d^{2}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{2}}}&=8{,}558595,\\{\frac {d^{2}b_{\frac {1}{2}}^{(3)}}{d\alpha ^{2}}}&=9{,}112527,&{\frac {d^{2}b_{\frac {1}{2}}^{(4)}}{d\alpha ^{2}}}&=9{,}107400,&{\frac {d^{2}b_{\frac {1}{2}}^{(5)}}{d\alpha ^{2}}}&=8{,}634030,\\{\frac {d^{2}b_{\frac {1}{2}}^{(6)}}{d\alpha ^{2}}}&=7{,}842733\,;&&&&\\\\{\frac {d^{3}b_{\frac {1}{2}}^{(0)}}{d\alpha ^{3}}}&=56{,}55335,&{\frac {d^{3}b_{\frac {1}{2}}^{(1)}}{d\alpha ^{3}}}&=57{,}35721,&{\frac {d^{3}b_{\frac {1}{2}}^{(2)}}{d\alpha ^{3}}}&=58{,}19633,\\{\frac {d^{3}b_{\frac {1}{2}}^{(3)}}{d\alpha ^{3}}}&=62{,}87646,&{\frac {d^{3}b_{\frac {1}{2}}^{(4)}}{d\alpha ^{3}}}&=66{,}32409,&{\frac {d^{3}b_{\frac {1}{2}}^{(5)}}{d\alpha ^{3}}}&=70{,}54326\,;\\\\b_{\frac {3}{2}}^{(0)}&=9{,}992539,&b_{\frac {3}{2}}^{(1)}&=8{,}871894,&b_{\frac {3}{2}}^{(2)}&=7{,}386580,\\b_{\frac {3}{2}}^{(3)}&=5{,}953940,&b_{\frac {3}{2}}^{(4)}&=4{,}704321,&b_{\frac {3}{2}}^{(5)}&=3{,}652052\,;\\\\\end{alignedat}}}
d
b
3
2
(
3
)
d
α
=
56,654
40
,
d
b
3
2
(
4
)
d
α
=
50,902
90.
{\displaystyle {\frac {db_{\frac {3}{2}}^{(3)}}{d\alpha }}=56{,}65440,\qquad {\frac {db_{\frac {3}{2}}^{(4)}}{d\alpha }}=50{,}90290.}
