A note on the inversion of power series
A note on the inversion of power series
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关于幂级数反演的一个注记
DOI：
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发表时间：
1947
期刊：
影响因子：
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通讯作者：
H. Chernoff
中科院分区：
文献类型：
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作者：
H. Chernoff
在这种情况下，存在两种长方法之间的选择。面对这个问题的计算机经常可以导出所需系数的显式公式并直接代入。这种方法的缺点是用公式代替时经常遇到的，即计算通常是不系统的，因此变得繁琐和容易出错。此外，公式变得非常长和复杂的系数可观的订单。1本文的主要目的在于提出一种方法，这将是特别有用的人谁不愿意推导复杂的公式或经历的考验，取代他们。将提出的方法将使计算机能够仅使用一页计算来获得逆幂级数的n个系数，大约J（n +1）2个数字。这种方法除了结构紧凑外，还具有系统性的优点。此外，类似的方法可以很容易地获得最正式的计算与幂级数。
At such times there exists a choice between two long methods. The computer who is faced with this problem very often may derive explicit formulae for the desired coefficients and substitute directly. This method has the drawback usually encountered in substituting in formulae, namely that the computations are usually unsystematic and therefore become tedious and subject to many errors. Furthermore the formulae become extremely long and complicated for coefficients of appreciable order.1 The chief purpose of this paper lies in presenting a method which will be especially useful to the person who is unwilling to derive complicated formulae or undergo the ordeal of substituting in them. The method which will be presented will enable the computer to obtain « coefficients of the inverse power series using only one page of computations with approximately J(n + l)2 numbers. Besides being compact, this method has the advantage of being systematic. Furthermore similar methods can be easily obtained for most formal calculations with power series.