THE SINGULAR INTEGRAL EQUATIONS CONTAINING BOTH COSECANT AND CONVOLUTION KERNEL WITH PERIODICITY
具周期性的含卷积核与余割核混合的积分方程

In this paper, a kind of singular integral equation containing both cosecant and convolution kernel with periodicity in class $L_2-\pi, \pi]$ is discussed. The problem is turned into simple discrete equation or jumping problem, by using the theory of discrete Fourier transform. The explicit representation of general solution in class $L_2-\pi, \pi]$ as well as the condition of solvability are obtained.