关于奇异积分的一个换序公式

A Formula for Changing Order of Integration on for Singular Integrals

从著名的B -P 公式出发 ,讨论了一个二阶奇异积分和一个Cauchy主值积分的累次积分的换序问题 ,得到如下积分换序公式 :∫Ldt(t-t0 ) 2∫Lf(t,τ)τ -tdτ=-π2 ddtf(t,t) ｜t=t0 + ∫Ldτ∫Lf(t,τ)(t-t0 ) 2 (τ-t) dt,t0

In this paper we discuss the problem of changing order of integration for singular integrals.From the famous B.-P. formula,we get a formula for changing order of integration for singular integrals as below:∫_Ldt(t-t_0)~2∫_Lf(t,τ)τ-tdτ=-π~2ddt f(t,t)_(｜t=t_0)+∫_Ldτ∫_Lf(t,τ)(t-t_0)~2(τ-t)dt,t_0∈L.