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Annales de mathématiques pures et appliquées, 1819-1820, Tome 10.djvu/376
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366
INTÉGRATION APPROCHÉE
−
n
(
720
+
3528
n
+
9744
n
2
+
17640
n
3
+
21000
n
4
+
15120
n
5
+
5040
n
6
)
Δ
7
q
+
n
(
5040
+
26136
n
+
78792
n
2
+
162456
n
3
+
2325200
n
4
+
231840
n
5
+
741120
n
6
+
40320
n
7
)
Δ
8
q
−
n
(
40320
+
219168
n
+
708744
n
2
+
161481
n
3
+
2693880
n
4
+
3265920
n
5
+
2731840
n
6
+
1451520
n
7
+
362880
n
8
)
Δ
9
q
+
n
(
362880
+
2053152
n
+
7036200
n
2
+
17368320
n
3
+
32319000
n
4
+
45554560
n
5
+
47628000
n
6
+
35078400
n
7
+
16329600
n
8
+
3628800
n
9
)
Δ
10
q
−
n
(
3628800
+
21257280
n
+
76521456
n
2
+
201828000
n
3
+
410031600
n
4
+
649479600
n
5
+
795175920
n
6
+
731808000
n
7
+
479001600
n
8
+
199584000
n
9
+
39916800
n
10
)
Δ
11
q
+
n
(
39916800
+
241087680
n
+
905507856
n
2
+
2526193824
n
3
+
5519487600
n
4
+
9604465200
n
5
+
13293292320
n
6
+
14411295360
n
7
+
11855289600
n
8
+
6985440000
n
9
+
2634508800
n
10
+
479001600
n
11
)
Δ
12
q
{\displaystyle {\begin{aligned}&-n\left(720+3528n+9744n^{2}+17640n^{3}+21000n^{4}\right.\\&\qquad \left.+15120n^{5}+5040n^{6}\right)\Delta ^{7}q\\&+n\left(5040+26136n+78792n^{2}+162456n^{3}+2325200n^{4}\right.\\&\qquad \left.+231840n^{5}+741120n^{6}+40320n^{7}\right)\Delta ^{8}q\\&-n\left(40320+219168n+708744n^{2}+161481n^{3}\right.\\&\qquad +2693880n^{4}+3265920n^{5}+2731840n^{6}\\&\qquad \left.+1451520n^{7}+362880n^{8}\right)\Delta ^{9}q\\&+n\left(362880+2053152n+7036200n^{2}+17368320n^{3}\right.\\&\qquad +32319000n^{4}+45554560n^{5}+47628000n^{6}\\&\qquad \left.+35078400n^{7}+16329600n^{8}+3628800n^{9}\right)\Delta ^{10}q\\&-n\left(3628800+21257280n+76521456n^{2}+201828000n^{3}\right.\\&\qquad +410031600n^{4}+649479600n^{5}+795175920n^{6}\\&\qquad +731808000n^{7}+479001600n^{8}+199584000n^{9}\\&\qquad \left.+39916800n^{10}\right)\Delta ^{11}q\\&+n\left(39916800+241087680n+905507856n^{2}\right.\\&\qquad +2526193824n^{3}+5519487600n^{4}+9604465200n^{5}\\&\qquad +13293292320n^{6}+14411295360n^{7}+11855289600n^{8}\\&\qquad \left.+6985440000n^{9}+2634508800n^{10}+479001600n^{11}\right)\Delta ^{12}q\\\end{aligned}}}