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Annales de mathématiques pures et appliquées, 1819-1820, Tome 10.djvu/381
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371
DES ÉQUATIONS DIFFÉRENTIELLES.
7.
o
Coefficient
G.
G
=
Δ
6
q
−
−
(
21
+
7
n
)
Δ
7
q
+
(
322
+
169
n
+
56
n
2
)
Δ
8
q
−
(
4536
+
3822
n
+
2016
n
2
+
504
n
3
)
Δ
9
q
+
(
63273
+
16150
n
+
48720
n
2
+
22680
n
3
+
5040
n
4
)
Δ
10
q
−
(
902055
+
1104411
n
+
1016400
n
2
+
665280
n
3
+
277200
n
4
+
55440
n
5
)
Δ
11
q
+
(
13339535
+
18462906
n
+
20015688
n
2
+
16465680
n
3
+
9702000
n
4
+
3659040
n
5
+
665280
n
6
)
Δ
12
q
{\displaystyle {\begin{aligned}G&=\Delta ^{6}q--(21+7n)\Delta ^{7}q+\left(322+169n+56n^{2}\right)\Delta ^{8}q\\&-\left(4536+3822n+2016n^{2}+504n^{3}\right)\Delta ^{9}q\\&+\left(63273+16150n+48720n^{2}+22680n^{3}+5040n^{4}\right)\Delta ^{10}q\\&-\left(902055+1104411n+1016400n^{2}+665280n^{3}+277200n^{4}\right.\\&\qquad \left.+55440n^{5}\right)\Delta ^{11}q\\&+\left(13339535+18462906n+20015688n^{2}+16465680n^{3}\right.\\&\qquad \left.+9702000n^{4}+3659040n^{5}+665280n^{6}\right)\Delta ^{12}q\\\end{aligned}}}
8.
o
Coefficient
H.
H
=
Δ
7
q
−
(
28
+
8
n
)
Δ
8
q
+
(
546
+
288
n
+
72
n
2
)
Δ
9
q
+
(
9450
+
6960
n
+
3240
n
2
+
720
n
3
)
Δ
10
q
+
(
157773
+
145200
n
+
95040
n
2
+
39600
n
3
+
7920
n
4
)
Δ
11
q
−
(
2637558
+
2859384
n
+
2352241
n
2
+
1386000
n
3
+
322720
n
4
+
95040
n
5
)
Δ
12
q
{\displaystyle {\begin{aligned}H&=\Delta ^{7}q-(28+8n)\Delta ^{8}q+\left(546+288n+72n^{2}\right)\Delta ^{9}q\\&+\left(9450+6960n+3240n^{2}+720n^{3}\right)\Delta ^{10}q\\&+\left(157773+145200n+95040n^{2}+39600n^{3}+7920n^{4}\right)\Delta ^{11}q\\&-\left(2637558+2859384n+2352241n^{2}+1386000n^{3}\right.\\&\qquad \left.+322720n^{4}+95040n^{5}\right)\Delta ^{12}q\\\end{aligned}}}
9.
o
Coefficient
I.
I
=
Δ
8
q
−
(
36
+
9
n
)
Δ
9
q
+
(
870
+
405
n
+
90
n
2
)
Δ
10
q
−
(
18150
+
11880
n
+
4950
n
2
+
990
n
3
)
Δ
11
q
+
(
357423
+
294030
n
+
173250
n
2
+
65340
n
3
+
11880
n
4
)
Δ
12
q
{\displaystyle {\begin{aligned}I&=\Delta ^{8}q-(36+9n)\Delta ^{9}q+\left(870+405n+90n^{2}\right)\Delta ^{10}q\\&-\left(18150+11880n+4950n^{2}+990n^{3}\right)\Delta ^{11}q\\&+\left(357423+294030n+173250n^{2}+65340n^{3}+11880n^{4}\right)\Delta ^{12}q\\\end{aligned}}}
10.
o
Coefficient
K.
K
=
Δ
9
q
−
(
45
+
10
n
)
Δ
10
q
+
(
1320
+
550
n
+
110
n
2
)
Δ
11
q
+
(
32670
+
19250
n
+
7260
n
2
+
1320
n
3
)
Δ
12
q
{\displaystyle {\begin{aligned}K&=\Delta ^{9}q-(45+10n)\Delta ^{10}q+\left(1320+550n+110n^{2}\right)\Delta ^{11}q\\&\qquad +\left(32670+19250n+7260n^{2}+1320n^{3}\right)\Delta ^{12}q\\\end{aligned}}}