柯西变换与某些级数的和(英文)

Cauchy Transform and the Sum of Some Series

定义柯西变换F(z)=∫_k dμ(w)/(z-w),z∈C\K,其中,K是顶点为{e^(izkπ/n)}(k=0)(n-1)的正多边形.通过对此柯西变换的研究,得到了某些级数的和.

The Cauchy transfrom of u on K by F（z）=∫_k dμ（w）/（z-w） for z∈C／K is defined,where K is a regular n-polygon with vertices {e^izkπ/n}（k=0）（n-1）, then the sums of some series through this Cauchy transform are obtained.