柯西积分公式的一点注记

A Note on Cauchy Integral Formula

摘要: 本文从例3.2计算积分出发，用参数方程法计算例3.2的积分值，并分别从积分曲线和被积函数两方面对例3.2进行推广。首先，把积分曲线进行推广，从以z₀为中心r为半径的圆推广到包含z₀的任一条闭曲线，推广后具有更广的适用范围。其次，把被积函数进行推广，由分别推广到及，进一步讨论了例3.2与柯西积分公式和解析函数高阶导数公式之间的密切联系。

Abstract: In this paper, according to integral calculation based on in Example 3.2, the integral value of Example 3.2 is calculated by the parametric equation method and the case 3.2 is general-ized from the integral curve and the integrand function. First, the integral curve is generalized, and the circle with z₀ as the center and r as the radius is generalized to any closed curve containing z₀; after the promotion, this example has a wider scope of application. Secondly, the integrand function is promoted, is promoted to and respectively, the close relationship between the case 3.2 and the Cauchy integral formula and the high-order derivative formula of the analytic function is discussed further.