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Annales de mathématiques pures et appliquées, 1826-1827, Tome 17.djvu/94
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(12)
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{\displaystyle \quad \left\{{\begin{aligned}\mathrm {pour\ } &\operatorname {\operatorname {Sin} } .bx=0,\\&x=0,\quad x=\pm {\frac {\varpi }{b}},\quad x=\pm {\frac {2\varpi }{b}},\ldots x=\pm {\frac {n\varpi }{b}},\ldots \,;\\\\\mathrm {pour\ } &\operatorname {\operatorname {Cos} } .bx=0,\\&x=\pm {\frac {\varpi }{2b}},\quad x=\pm {\frac {3\varpi }{2b}},\ldots x=\pm {\frac {(2n+1)\varpi }{2b}},\ldots \,;\\\\\mathrm {pour\ } &e^{bx}=h+k{\sqrt {-1}},\\&x={\frac {1}{b}}\left[\operatorname {l} (\rho )+\left({\frac {\varpi }{2}}-\omega \right){\sqrt {-1}}\pm 2n\varpi {\sqrt {-1}}\right]\,;\\\\\mathrm {pour\ } &e^{bx{\sqrt {-1}}}h+k{\sqrt {-1}},\\&x={\frac {1}{b}}\left[{\frac {\varpi }{2}}-\omega -{\sqrt {-1}}.\operatorname {l} (\rho )\pm 2n\varpi \right]\,;\\\\\mathrm {pour\ } &e^{\left(a+b{\sqrt {-1}}\right)x}=h+k{\sqrt {-1}},\\&x={\frac {\operatorname {l} (\rho )+\left({\frac {\pi }{2}}-\omega \right){\sqrt {-1}}\pm 2n\varpi {\sqrt {-1}}}{a+b{\sqrt {-1}}}}\,;\\\\\mathrm {pour\ } &\operatorname {l} (1+re^{bx{\sqrt {-1}}}=1,\\\\&x=\pm {\frac {2n\pi }{b}}-{\frac {\sqrt {-1}}{b}}\operatorname {l} {\frac {\varepsilon -1}{r}}\,;\end{aligned}}\right.}
[
1
]
et ainsi du reste.
↑
Voy le Cours d’analyse algébrique, chap. IX, (12) et (22).
![{\displaystyle \quad \left\{{\begin{aligned}\mathrm {pour\ } &\operatorname {\operatorname {Sin} } .bx=0,\\&x=0,\quad x=\pm {\frac {\varpi }{b}},\quad x=\pm {\frac {2\varpi }{b}},\ldots x=\pm {\frac {n\varpi }{b}},\ldots \,;\\\\\mathrm {pour\ } &\operatorname {\operatorname {Cos} } .bx=0,\\&x=\pm {\frac {\varpi }{2b}},\quad x=\pm {\frac {3\varpi }{2b}},\ldots x=\pm {\frac {(2n+1)\varpi }{2b}},\ldots \,;\\\\\mathrm {pour\ } &e^{bx}=h+k{\sqrt {-1}},\\&x={\frac {1}{b}}\left[\operatorname {l} (\rho )+\left({\frac {\varpi }{2}}-\omega \right){\sqrt {-1}}\pm 2n\varpi {\sqrt {-1}}\right]\,;\\\\\mathrm {pour\ } &e^{bx{\sqrt {-1}}}h+k{\sqrt {-1}},\\&x={\frac {1}{b}}\left[{\frac {\varpi }{2}}-\omega -{\sqrt {-1}}.\operatorname {l} (\rho )\pm 2n\varpi \right]\,;\\\\\mathrm {pour\ } &e^{\left(a+b{\sqrt {-1}}\right)x}=h+k{\sqrt {-1}},\\&x={\frac {\operatorname {l} (\rho )+\left({\frac {\pi }{2}}-\omega \right){\sqrt {-1}}\pm 2n\varpi {\sqrt {-1}}}{a+b{\sqrt {-1}}}}\,;\\\\\mathrm {pour\ } &\operatorname {l} (1+re^{bx{\sqrt {-1}}}=1,\\\\&x=\pm {\frac {2n\pi }{b}}-{\frac {\sqrt {-1}}{b}}\operatorname {l} {\frac {\varepsilon -1}{r}}\,;\end{aligned}}\right.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/38b91014d17837b5f21f951f9d9ae9b7390b576e)
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