奇异积分方程相伴多项式公共零点的探讨

The Common Zero Point(s) of Associated Polynomials of Singular Integeral Equation

首先分析了权函数为偶函数时正交多项式的性质 ,继而证明了相伴正交多项式公共零点的存在性 ,并给出了一个充分条件 .对要求更为宽松的相伴正交多项式公共零点的存在性 ,也给出了例子及充分条件 .

This article first analysizes the property of orthogonal polynomial when weight function is even, then proves the existence of commom zero point of associated orthogonal polynomials and present a sufficient condition. On the existence of common zero point of associated polynomails which needs less requirement, this article also presents example and sufficient condition.