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A relatively direct method is expounded in this paper to prove the termwise differentiation of power series, and a simple method is expressed to calculate the Fourier coefficient.

用比较直接方法证明幂和函在收敛域可以逐项微分；得到了计算傅立叶系一种简便方法.

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And, in this case, it's an infinite polynomial so  I should really be calling it a power series.

而且，在这种情，是个项式的级数，所以我应该称之为幂级数。

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