利用微分公式求无穷级数和的一种简便方法
A succinct method for investigating the sums of infinite series through differential formulae
摘要：
翻译的“Methodus succincta summas serierum infinitarum per formulations differentiales investigandi”（1780）。欧拉想用不同的方法表示某个给定的函数项级数S（x）=X（x）+X（x+1）+X（x+2）+等。他写S作为一系列衍生物的X与未知系数。他从这些系数中得到一个生成函数V（z），这与涉及伯努利数的生成函数相同。
英文摘要：
Translation of "Methodus succincta summas serierum infinitarum per formulas differentiales investigandi" (1780). Euler wants to represent some given series of functions S(x)=X(x)+X(x+1)+X(x+2)+etc. in a different way. He writes S as a series in derivatives of X with unknown coefficients. He makes a generating function V(z) out of these coefficients, which is the same as a generating function that involves the Bernoulli numbers.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
