一类新的二元多项式的概率原点
A Probablistic Origin for a New Class of Bivariate Polynomials
摘要：
我们在这里提出了一种概率方法来生成新的多项式在两个离散变量。这扩展了我们以前的工作“经典的”正交多项式在以前未探索的方向，导致发现一个完全可溶的本征值问题对应的二元马尔可夫链的过渡内核形成的卷积简单的二项式和三项分布。相关的本征函数问题的解决方案，给出了核的谱分解，导致我们认为是一类新的正交多项式在两个离散变量。讨论了这种方法推广的可能性。
英文摘要：
We present here a probabilistic approach to the generation of new polynomials in two discrete variables. This extends our earlier work on the 'classical' orthogonal polynomials in a previously unexplored direction, resulting in the discovery of an exactly soluble eigenvalue problem corresponding to a bivariate Markov chain with a transition kernel formed by a convolution of simple binomial and trinomial distributions. The solution of the relevant eigenfunction problem, giving the spectral resolution of the kernel, leads to what we believe to be a new class of orthogonal polynomials in two discrete variables. Possibilities for the extension of this approach are discussed.
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