实轴上含有极点的有理函数积分及其Cauchy主值  

On the Integrals of Rational Functions When Having Pole in the Real Axis and Their Cauchy Principal Value

作　　者：李志荣[1] 

机构地区：[1]揭阳职业技术学院数学与计算机系,广东揭阳522000

出　　处：《海南大学学报（自然科学版）》2004年第3期209-212,共4页Natural Science Journal of Hainan University

摘　　要：对复分析中有理函数的积分条件进行削弱.讨论有理函数R(z)在半实轴x≥0上无极点时的反常积分;R(z)在半实轴x≥0上只有简单极点z=1时的反常积分的Cauchy主值(P.V.).建立 R(x)dx(或其Cauchy主值)与残数间的关系式定理.Based on the weakening term of the integral complex analysis, this paper discusses abnormal integrals of the rational function R(z) without pole in the semi-real axis x≥0; also discusses the Cauchy principal value(P. V. ) of the abnormal integrals when R(z) only has pole z = 1 in the semi-real axis x≥ 0; further,presents the theorem of relational expression between R(x)dx (or the Cauchy principal value) and the residues.

关 键 词：有理函数 反常积分 柯西主值 极点 复分析 

分 类 号：O174.5[理学—数学]