简单弧上带Cauchy核的第一类奇异积分方程的新解法

The New Method of Solving the First Category of Singular Intergral Equation with Cauchy Core Along Simple Curve

提供了简单弧上带Cauchy核的第一类奇异积分方程1πi∫ltf-(tt)0dt+21πi∫lk(t,t0)f(t)dt=g(t0)的一个新解法,给出了解的具体表达式与运算实例.本文的方法可应用于更广泛的情形.其中k(t,t0)为多项式,t0∈l,t0不为l的端点,f(t)在端点的奇性不到一阶.

This paper mainly supply a new method of solving the first category of singular intergral equation with Cauchy core along simple curve 1/πi∫l f（t）/t-t0dt＋1/2πi∫lk（t,t0）f（t）dt=g（t0） also show the solution＇s specific expression and caculating example. The method of this paper can be used in more wide situation. While k（t,t0） is polynomial, t0 belongs to t, but is not the end point, the order of f（t） at the end point is smaller than one.