On regular singular points of linear differential equations of the second order whose coefficients are not necessarily analytic
On regular singular points of linear differential equations of the second order whose coefficients are not necessarily analytic
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关于系数不一定解析的二阶线性微分方程的正则奇异点
DOI：
10.1090/s0002-9947-1900-1500523-9
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通讯作者：
M. Bôcher
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作者：
M. Bôcher
自柯西时代以来，人们就认为建立微分方程解的存在性很有意义，该微分方程的系数是实变量x的函数，并且不需要这些系数是x的解析函数，而只是连续函数。这种观点的自然延伸是希望研究此类方程的奇异点的性质，即。即系数变得不连续的点。本文的目的是在一个特殊但同时又重要的案例中进行这样的调查。我们将把自己限制在等式中：
Ever since the time of CAUCHY it has been considered of interest to establish the existence of solutions of differential equations whose coefficients are funetioiis of a real variable x, and to do this without requiring these coefficients to be analytic functions of x, but merely continuous functions. It is a natural extension of this point of view to wislh to investigate the nature of singular points of such equations, i. e., of points where the coefficients become discontinuous.t It is my object in the present paper to carry through such an investigation in a special, but at the same time important, case. We shall confine ourselves to the equation: