论文标题
两个可变的弗洛伊德正交多项式和矩阵painlevé-type差异方程
Two variable Freud orthogonal polynomials and matrix Painlevé-type difference equations
论文作者
论文摘要
我们研究了与弗洛伊德重量功能相关的双变量正交多项式，具体取决于实际参数。我们分析了正交多项式的三个项关系的矩阵系数，以及这些双变量半经典正交多项式满足的结构关系的系数，也是矩阵差异差异方程，也用于双变量正交多种元素。获得了painlevé方程的三个任期关系系数与双变量案例的系数的扩展，并获得了langmuir晶格的二维版本。
We study bivariate orthogonal polynomials associated with Freud weight functions depending on real parameters. We analyze relations between the matrix coefficients of the three term relations for the orthonormal polynomials as well as the coefficients of the structure relations satisfied by these bivariate semiclassical orthogonal polynomials, also a matrix differential-difference equation for the bivariate orthogonal polynomials is deduced. The extension of the Painlevé equation for the coefficients of the three term relations to the bivariate case and a two dimensional version of the Langmuir lattice are obtained.
