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中文摘要：
柯西积分公式是复变函数论中的重要公式之一。首先用极限方法给出并证明了含无穷远点区域的柯西积分公式;然后采取添加积分路径的方式,将含无穷远点区域转化为有限区域研究,再取极限将有限区域扩展为含无穷远点区域的方法,将含无穷远点区域的柯西积分公式推广到被积函数含多个极点的情况。计算实例表明,含无穷远点区域的柯西积分公式及其推广形式适用有效,方便积分的计算。
英文摘要：
Cauchy integral formula is one of the most important formulas in complex variable theory.In this paper,the Cauchy integral formula in the region with infinite point is firstly given and proven by limit.Then the region with infinite far point is transformed into limited area,and the Cauchy integral formula in the region with infinite point is extended to the formula,of which the integrand has multiple poles.Calculation examples show that Cauchy integral formula in the region with infinite point and its extension are an effective and convenient way for integral calculation.
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