A Combinatorial Approach to Biorthogonal Polynomials
A Combinatorial Approach to Biorthogonal Polynomials
复制标题
双正交多项式的组合方法
DOI：
10.1137/0405032
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发表时间：
1992
期刊：
影响因子：
--
通讯作者：
Dongsu Kim
中科院分区：
文献类型：
--
作者：
Dongsu Kim
证明了双正交多项式具有系数之间存在一定关系的递推关系。基于双正交多项式的这些递推关系，双正交多项式被解释为直线中某些路径的集合的权重，并且所涉及的线性函数的矩被解释为平面中某些路径的集合的权重。这种解释是维诺对一般正交多项式解释的推广。
It is proved that biorthogonal polynomials are characterized by the recurrence relations whose coefficients are related in a certain way. On the basis of these recurrence relations for biorthogonal polynomials, biorthogonal polynomials are interpreted as weights of sets of certain paths in the line, and the moments of the linear functional involved as weights of sets of certain paths in the plane. This interpretation is a generalization of Viennot’s interpretation of general orthogonal polynomials.