柯西积分公式的一点注记

A Note on Cauchy Integral Formula

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。

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.