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Math Help - Power series help

  1. #1
    Junior Member
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    Power series help

    I need to show that if you expand x(t,\varepsilon)=(1-\varepsilon^2)^{-\frac{1}{2}}e^{-\varepsilon t}sin[(1-\varepsilon^2)^{\frac{1}{2}}t] as a power series in \varepsilon, you get x(t,\varepsilon)=sint-\varepsilon t sint+O(\varepsilon^2)

    Any help is appreciated. Thanks!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by splash View Post
    I need to show that if you expand x(t,\varepsilon)=(1-\varepsilon^2)^{-\frac{1}{2}}e^{-\varepsilon t}sin[(1-\varepsilon^2)^{\frac{1}{2}}t] as a power series in \varepsilon, you get x(t,\varepsilon)=sint-\varepsilon t sint+O(\varepsilon^2)

    Any help is appreciated. Thanks!
    Taylor series:

    <br />
x(t,\varepsilon)=x(t,0)+\varepsilon\, \frac{\partial x}{\partial \varepsilon}(x,0)+O(\varepsilon^2)<br />

    RonL
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