1) Cauchy principal value
Cauchy主值
1.
By using the multiple-valued character of the function zp(-1<p<1,p≠0) and logz,this paper discusses generalized integrals ∫+∞0xpR(x)dx and their Cauchy principal value when the rational function R(z) without the pole,or only has simple pole,in the path,gain the theorem of relational expression between ∫+∞0R(x)dx(or the Cauchy principal value) and the residues.
利用函数zp(-1Cauchy主值,得到∫0+∞xpR(x)dx(或其Cauchy主值)与残数间的关系式定理。
2.
In this paper, the Cauchy principal value of integrals ∫from 0 to ∞(R(x)logxdx) with rational function R(z) having simple pole in the semi-real axis x≥0 is discussed.
首先讨论有理函数R(z)在半实轴x≥0上含有简单极点时积分∫from x=0 to ∞(R(x)logxdx)的Cauchy主值,然后讨论积分∫from x=0 to ∞(R(x)(logx)~2dx)的Cauchy主值,得到这些积分主值的计算公式。
3.
This article\'s prime task is solves the shape like type ∫∞-∞eaxf(ex)dx on the generalized integrals of meromorphic functions and their Cauchy principal value summation problem.
运用留数定理求解形如∫-∞∞eaxf(ex)dx的一类亚纯函数的广义积分及其Cauchy主值的和,得到∫-∞∞eaxf(ex)dx(Cauchy主值)与留数间的关系。
2) Cauchy Principle
Cauchy主值积分
1.
In this paper,we first introduces some notations and some preliminary results,then we give quadrature rules with Cauchy Principle integral on the unit circle for some Chebyshev weight functions,at that time we give their error bounds.
在本文中,我们首先给出一些基本的结果和一些概念,然后给出单位圆上带Cheby shev权的一些Cauchy主值积分的求积公式,最后给出了它们的误差估计。
3) Cauchy principle value of integral
Cauchy积分主值
4) Cauchy type singular integral
Cauchy型主值积分
1.
In this paper, the author first gives a kind quadrature rule Φm*(ωf,x) for Cauchy type singular integral Φ(ωf, x), then proves the sequence{Φm*(ωf,x)}m=2∞ ls uniformly convergent to Φ(ωf,x) on the interval [-1,1], at that time gives its error bounds.
该文首先给出Cauchy型主值积分Φ(ωf,x)的一种求积公式Φm*(ωf,x),然后证明序列 {Φm*(ωf,x)}m=2∞在整个闭区间[-1,1]上是一致收敛到Cauchy型主值积分Φ(ωf,x)的,同时给出它的误差界。
5) Cauchy's principal value of singular integral
奇异积分的Cauchy主值
6) Cauchy's theorem on mean value
Cauchy均值定理
补充资料：主后
1.同"主后"。
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