论文标题
平面立方曲线的正交多项式
Orthogonal polynomials on planar cubic curves
论文作者
论文摘要
考虑了立方曲线上两个变量的正交多项式，包括椭圆曲线的情况。对于在立方曲线上定义的适当权重函数的积分，正交多项式的明确基础是根据一个变量中的两个正交多项式族的家族构建的。我们表明，这些正交多项式可用于近似于立方体和方形奇异性的函数，并证明了它们用奇异溶液求解微分方程的用法。
Orthogonal polynomials in two variables on cubic curves are considered, including the case of elliptic curves. For an integral with respect to an appropriate weight function defined on a cubic curve, an explicit basis of orthogonal polynomials is constructed in terms of two families of orthogonal polynomials in one variable. We show that these orthogonal polynomials can be used to approximate functions with cubic and square root singularities, and demonstrate their usage for solving differential equations with singular solutions.
