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Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/250
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3
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{
c
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1
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e
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4
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2
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m
)
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5
2
e
′
2
]
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B
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5
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γ
2
m
2
}
{\displaystyle +{\frac {3m^{2}}{a_{\text{ı}}}}\left\{{\begin{aligned}&{\frac {c}{4}}\left[1+{\frac {e^{2}}{4}}(2-19m)-{\frac {5}{2}}e'^{2}\right]\\\\-&{\frac {3+4m}{4}}\left(1+{\frac {1}{2}}e^{2}-{\frac {5}{2}}e'^{2}\right)+{\frac {1-c^{2}}{4(1-m)}}\\\\-&{\frac {2(1+m)}{2-2m-c}}\left(1+{\frac {7}{4}}e^{2}-{\frac {5}{2}}e'^{2}\right)\\\\-&{\frac {1}{2}}{\rm {\left(A_{1}^{(1)}-2A_{2}^{(0)}\right)+{\frac {1}{2}}\left(B_{2}^{(5)}-B_{2}^{(6)}\right)}}{\frac {\gamma ^{2}}{m^{2}}}\end{aligned}}\right\}}
×
e
cos
(
2
v
−
2
m
v
−
c
v
+
ϖ
)
{\displaystyle \times e\cos(2v-2mv-cv+\varpi )}
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m
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4
a
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(
3
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c
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4
m
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8
(
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2
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2
A
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2
)
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e
cos
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m
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c
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ϖ
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3
m
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a
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4
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m
2
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m
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2
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1
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9
)
γ
2
m
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2
A
2
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3
)
)
e
′
cos
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v
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m
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′
)
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3
m
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a
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7
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4
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3
m
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2
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3
m
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2
B
1
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10
)
γ
2
m
2
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2
A
2
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4
)
)
e
′
cos
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m
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+
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)
{\displaystyle {\begin{aligned}&-{\frac {3m^{2}}{4a_{\text{ı}}}}\left(3+c-4m+{\frac {8(1-m)}{2-2m+c}}+2{\rm {A}}_{2}^{(2)}\right)e\cos(2v-2mv+cv-\varpi )\\\\&-{\frac {3m^{2}}{4a_{\text{ı}}}}\left({\frac {4-m}{2-m}}+2{\rm {B}}_{1}^{(9)}{\frac {\gamma ^{2}}{m^{2}}}+2{\rm {A}}_{2}^{(3)}\right)e'\cos(2v-2mv+c'mv-\varpi ')\\\\&+{\frac {3m^{2}}{4a_{\text{ı}}}}\left({\frac {7(4-3m)}{2-3m}}-2{\rm {B}}_{1}^{(10)}{\frac {\gamma ^{2}}{m^{2}}}-2{\rm {A}}_{2}^{(4)}\right)e'\cos(2v-2mv-c'mv+\varpi ')\end{aligned}}}
+
{
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8
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B
1
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8
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3
2
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+
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)
A
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2
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(
3
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(
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3
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A
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(
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3
m
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A
2
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1
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(
B
1
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9
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B
1
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10
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2
m
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2
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5
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−
11
C
2
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6
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2
C
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9
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2
C
2
(
10
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}
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m
a
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[
4
A
2
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3
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5
2
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e
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]
}
{\displaystyle +\left\{{\begin{aligned}&\left\{{\begin{aligned}1&+e^{2}+{\frac {\gamma ^{2}}{4}}+{\frac {9}{8}}e'^{2}+\left({\rm {B_{1}^{(7)}-B_{1}^{(8)}}}\right){\frac {\gamma ^{2}}{m^{2}}}-{\frac {3}{2}}(1+2m){\rm {A}}_{2}^{(0)}\\\\&-{\frac {2(1-2m)(3-2m)(3-m)}{(2-3m)(2-m)}}{\rm {A}}_{2}^{(0)}-2{\rm {A}}_{2}^{(3)}-(2-3m){\rm {A}}_{2}^{(1)}\\\\&+{\rm {\left(B_{1}^{(9)}+B_{1}^{(10)}\right)B_{1}^{(0)}}}{\frac {\gamma ^{2}}{m^{2}}}-{\rm {A_{2}^{(5)}-11C_{2}^{(6)}-2C_{2}^{(9)}+2C_{2}^{(10)}}}\end{aligned}}\right\}\\\\&+{\frac {6m}{a_{\text{ı}}}}\left[4A_{2}^{(0)}+A_{2}^{(3)}-A_{2}^{(4)}-10A_{1}^{(1)}e^{2}+{\frac {5}{2}}\left(A_{1}^{(7)}-A_{1}^{(6)}\right)e^{2}\right]\end{aligned}}\right\}}
×
e
′
cos
(
c
′
m
v
−
ϖ
′
)
{\displaystyle \times e'\cos(c'mv-\varpi ')}
+
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{
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c
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2
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m
2
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1
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1
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6
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m
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c
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A
1
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9
)
}
{\displaystyle +{\frac {3m^{2}}{2a_{\text{ı}}}}\left\{{\begin{aligned}&{\frac {3+2m-c}{4}}+{\frac {2+m}{2-m-c}}-{\frac {3}{2}}{\rm {A_{1}^{(1)}-A_{1}^{(6)}}}\\\\&-\left({\frac {3+m-c}{2}}+{\frac {4}{2-m-c}}\right){\rm {A_{1}^{(9)}}}\end{aligned}}\right\}}
×
e
e
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cos
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2
v
−
2
m
v
−
c
v
+
c
′
m
v
+
ϖ
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ϖ
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)
{\displaystyle \times ee'\cos(2v-2mv-cv+c'mv+\varpi -\varpi ')}
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m
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{
7
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3
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A
1
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8
)
}
{\displaystyle -{\frac {3m^{2}}{2a_{\text{ı}}}}\left\{{\begin{aligned}&{\frac {7(3+6m-c)}{4}}+{\frac {7(2+3m)}{2-3m-c}}+{\frac {3}{2}}{\rm {A_{1}^{(1)}}}\\\\&+{\rm {A_{1}^{(7)}}}+\left({\frac {3-m-c}{2}}+{\frac {4}{2-3m-c}}\right){\rm {A_{1}^{(8)}}}\end{aligned}}\right\}}
×
e
e
′
cos
(
2
v
−
2
m
v
−
c
′
m
v
+
ϖ
+
ϖ
′
)
{\displaystyle \times ee'\cos(2v-2mv-c'mv+\varpi +\varpi ')}
−
3
m
2
2
a
ı
{
+
3
+
2
m
2
−
(
1
+
2
m
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c
4
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2
c
+
m
)
A
1
(
1
)
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A
1
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8
)
+
(
1
+
3
m
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c
2
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4
c
+
m
)
A
1
(
7
)
}
{\displaystyle -{\frac {3m^{2}}{2a_{\text{ı}}}}\left\{{\begin{aligned}&+{\frac {3+2m}{2}}-\left({\frac {1+2m+c}{4}}+{\frac {2}{c+m}}\right){\rm {A_{1}^{(1)}}}\\\\&+{\rm {A_{1}^{(8)}}}+\left({\frac {1+3m+c}{2}}+{\frac {4}{c+m}}\right){\rm {A_{1}^{(7)}}}\end{aligned}}\right\}}
×
e
e
′
cos
(
c
v
+
c
′
m
v
−
ϖ
−
ϖ
′
)
{\displaystyle \times ee'\cos(cv+c'mv-\varpi -\varpi ')}
−
3
m
2
2
a
ı
{
+
3
−
2
m
2
+
A
1
(
9
)
+
7
(
1
+
2
m
+
c
4
+
2
c
−
m
)
A
1
(
1
)
+
(
1
+
m
+
c
2
+
4
c
−
m
)
A
1
(
6
)
}
{\displaystyle -{\frac {3m^{2}}{2a_{\text{ı}}}}\left\{{\begin{aligned}&+{\frac {3-2m}{2}}+{\rm {A_{1}^{(9)}}}+7\left({\frac {1+2m+c}{4}}+{\frac {2}{c-m}}\right){\rm {A_{1}^{(1)}}}\\\\&+\left({\frac {1+m+c}{2}}+{\frac {4}{c-m}}\right){\rm {A_{1}^{(6)}}}\end{aligned}}\right\}}
×
e
e
′
cos
(
c
v
−
c
′
m
v
−
ϖ
+
ϖ
′
)
{\displaystyle \times ee'\cos(cv-c'mv-\varpi +\varpi ')}