论文标题
Hahn多项式用于超几何分布
Hahn polynomials for hypergeometric distribution
论文作者
论文摘要
多元高几何分布的正交多项式在$ \ rr^d $中的多面体域中的晶格上定义。通过对具有负整数参数的经典HAHH多项式分析来研究它们的结构。探索了Hahn多项式的分解，并用于解释正交多项式的索引集与多面体结构域中的晶格之间的关系。在多变量的情况下，这些结构导致非平凡多项式的非平凡家族在晶格多面体上消失。还讨论了正交多项式的生成函数和双光谱性能。
Orthogonal polynomials for the multivariate hypergeometric distribution are defined on lattices in polyhedral domains in $\RR^d$. Their structures are studied through a detailed analysis of classical Hahn polynomials with negative integer parameters. Factorization of the Hahn polynomials is explored and used to explain the relation between the index set of orthogonal polynomials and the lattice set in polyhedral domain. In the multivariate case, these constructions lead to nontrivial families of hypergeometric polynomials vanishing on lattice polyhedra. The generating functions and bispectral properties of the orthogonal polynomials are also discussed.
