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Laplace - Œuvres complètes, Gauthier-Villars, 1878, tome 3.djvu/237
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n
o
1 donnera, par son développement,
3
m
2
a
ı
{
1
+
3
e
2
+
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2
4
−
5
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2
m
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(
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1
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4
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7
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−
10
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19
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8
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(
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19
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×
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17
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4
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2
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[
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+
1
+
9
2
e
2
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(
1
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a
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4
a
a
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(
1
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m
v
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}
{\displaystyle {\frac {3m^{2}}{a_{\text{ı}}}}\left\{{\begin{aligned}&{\frac {1+3e^{2}+{\frac {\gamma ^{2}}{4}}-{\frac {5}{2}}e'^{2}}{2-2m}}\cos(2v-2mv)\\+&\left[{\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)\right]\\&\qquad \qquad \qquad \qquad \times e\cos(2v-2mv-cv+\varpi )\\-&{\frac {2(1-m)}{2-2m+c}}e\cos(2v-2mv+cv-\varpi )\\+&{\frac {7e'}{2(2-3m)}}\cos(2v-2mv-c'mv+\varpi ')\\-&{\frac {e'}{2(2-m)}}\cos(2v-2mv+c'mv-\varpi ')\\-&{\frac {7(2+3m)}{2(2-3m-c)}}ee'\cos(2v-2mv-cv-c'mv+\varpi +\varpi ')\\-&{\frac {7(2-3m)}{2(2-3m+c)}}ee'\cos(2v-2mv-cv-c'mv+\varpi +\varpi ')\\+&{\frac {2+m}{2(2-m-c)}}ee'\cos(2v-2mv-cv+c'mv+\varpi -\varpi ')\\+&{\frac {2-m}{2(2-m+c)}}ee'\cos(2v-2mv+cv+c'mv-\varpi -\varpi ')\\-&{\frac {10+19m+8m^{2}}{4(2c-2+2m)}}e^{2}\cos(2cv-2v+2mv-2\varpi )\\+&{\frac {10-19m+8m^{2}}{4(2c+2-2m)}}e^{2}\cos(2cv+2v-2mv-2\varpi )\\+&\left[{\frac {4g^{2}-1}{16(1-m)}}-{\frac {2+m}{4(2g-2-2m)}}\right]\\&\qquad \qquad \qquad \qquad \qquad \times \gamma ^{2}\cos(2gv-2v+2mv-2\theta )\\+&\left[{\frac {4g^{2}-1}{16(1-m)}}+{\frac {2-m}{4(2g+2-2m)}}\right]\\&\qquad \qquad \qquad \qquad \qquad \times \gamma ^{2}\cos(2gv+2v-2mv-2\theta )\\+&{\frac {17e'^{2}}{2(2-4m)}}\cos(2v-2mv-2c'mv+2\varpi ')\\-&\left[{\frac {5+m}{4(2-2m-2g+c)}}+{\frac {3(1-m)}{4(2-2m+c)}}\right]\\&\qquad \qquad \qquad \times e\gamma ^{2}\cos(2v-2mv-2gv+cv+2\theta -\varpi )\\+&{\frac {1+{\frac {9}{2}}e^{2}+2e'^{2}}{4(1-m)}}{\frac {a}{a'}}\cos(v-mv)\\+&{\frac {1}{4}}{\frac {a}{a'}}e'\cos(v-mv+c'mv-\varpi ')\\+&{\frac {3}{4(1-2m)}}{\frac {a}{a'}}e'\cos(v-mv-c'mv+\varpi ')\end{aligned}}\right\}}
![{\displaystyle {\frac {3m^{2}}{a_{\text{ı}}}}\left\{{\begin{aligned}&{\frac {1+3e^{2}+{\frac {\gamma ^{2}}{4}}-{\frac {5}{2}}e'^{2}}{2-2m}}\cos(2v-2mv)\\+&\left[{\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)\right]\\&\qquad \qquad \qquad \qquad \times e\cos(2v-2mv-cv+\varpi )\\-&{\frac {2(1-m)}{2-2m+c}}e\cos(2v-2mv+cv-\varpi )\\+&{\frac {7e'}{2(2-3m)}}\cos(2v-2mv-c'mv+\varpi ')\\-&{\frac {e'}{2(2-m)}}\cos(2v-2mv+c'mv-\varpi ')\\-&{\frac {7(2+3m)}{2(2-3m-c)}}ee'\cos(2v-2mv-cv-c'mv+\varpi +\varpi ')\\-&{\frac {7(2-3m)}{2(2-3m+c)}}ee'\cos(2v-2mv-cv-c'mv+\varpi +\varpi ')\\+&{\frac {2+m}{2(2-m-c)}}ee'\cos(2v-2mv-cv+c'mv+\varpi -\varpi ')\\+&{\frac {2-m}{2(2-m+c)}}ee'\cos(2v-2mv+cv+c'mv-\varpi -\varpi ')\\-&{\frac {10+19m+8m^{2}}{4(2c-2+2m)}}e^{2}\cos(2cv-2v+2mv-2\varpi )\\+&{\frac {10-19m+8m^{2}}{4(2c+2-2m)}}e^{2}\cos(2cv+2v-2mv-2\varpi )\\+&\left[{\frac {4g^{2}-1}{16(1-m)}}-{\frac {2+m}{4(2g-2-2m)}}\right]\\&\qquad \qquad \qquad \qquad \qquad \times \gamma ^{2}\cos(2gv-2v+2mv-2\theta )\\+&\left[{\frac {4g^{2}-1}{16(1-m)}}+{\frac {2-m}{4(2g+2-2m)}}\right]\\&\qquad \qquad \qquad \qquad \qquad \times \gamma ^{2}\cos(2gv+2v-2mv-2\theta )\\+&{\frac {17e'^{2}}{2(2-4m)}}\cos(2v-2mv-2c'mv+2\varpi ')\\-&\left[{\frac {5+m}{4(2-2m-2g+c)}}+{\frac {3(1-m)}{4(2-2m+c)}}\right]\\&\qquad \qquad \qquad \times e\gamma ^{2}\cos(2v-2mv-2gv+cv+2\theta -\varpi )\\+&{\frac {1+{\frac {9}{2}}e^{2}+2e'^{2}}{4(1-m)}}{\frac {a}{a'}}\cos(v-mv)\\+&{\frac {1}{4}}{\frac {a}{a'}}e'\cos(v-mv+c'mv-\varpi ')\\+&{\frac {3}{4(1-2m)}}{\frac {a}{a'}}e'\cos(v-mv-c'mv+\varpi ')\end{aligned}}\right\}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/bd12f8140d08ca61bc76f9fbf63d4c59b987b0c9)
