复多值函数积分问题的探讨

以教材中的习题为例,探讨了复变函数中多值函数的积分计算问题.首先利用留数定理给出了例题1的解法1; 然后在割破平面确定单值解析分支的基础上,使用牛顿莱布尼兹公式给出了例题1的解法2, 并分析了影响解法1和解法2结果的因素; 最后,通过构建新的辅助函数计算了涅尔积分例题,从而推广了实积分的计算方法.

Discussion on integral problems of complex multivalued functions

Taking an exercise in textbooks as an example, this paper discusses the integral calculation of multivalued functions with complex variables. Firstly, the solution 1 of example 1 is given by residue theorem; secondly, the solution 2 of example 1 is given by using Newton Leibniz formula on the basis of cutting the plane to determine the single-valued analytic branch, and the factors affecting the results of solution 1 and solution 2 are analyzed; finally, the example of Nell integral is calculated by constructing a new auxiliary function, thus the calculation method of real integral is extended.