来自《耶鲁大学开放课程：基础物理 第16集 第16集》

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  And you go as far as you can.
  你想写多长就能写多长
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  If you know 13 derivatives, put 13 derivatives here.
  如果你知道十三个导数 就把它们写在这儿
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  That's an approximation.
  这就是一个近似
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  That's not called a Taylor series,
  但它还不是泰勒级数
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  that's the approximation to the function.
  只是函数的一个近似罢了
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  Now, it may happen that sometimes you hit the jackpot,
  有时候你会十分走运
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  and you know all the derivatives.
  你已知所有阶导数
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  Someone tells you all the derivatives of the function,
  有人告诉你这个函数的全部导数值
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  then why stop? Add them all up.
  不要犹豫 把它们全部加起来
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  Then, you will get the sum
  这样你就能到从零阶导数
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  going from the 0 derivative all the way up to infinity.
  直到无穷阶导数的和
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  And if you do the summation of every value of x, you will get a value,
  对每一个 x 值求和 你都能得到一个值