|
Эта публикация цитируется в 30 научных статьях (всего в 30 статьях)
A Probablistic Origin for a New Class of Bivariate Polynomials
Michael R. Hoare, Mizan Rahmana a School of Mathematics and Statistics, Carleton University, Ottawa, ON K1S 5B6, Canada
Аннотация:
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.
Ключевые слова:
cumulative Bernoulli trials; multivariate Markov chains; $9-j$ symbols; transition kernel; Askey–Wilson polynomials; eigenvalue problem; trinomial distribution; Krawtchouk polynomials.
Поступила: 15 сентября 2008 г.; в окончательном варианте 15 декабря 2008 г.; опубликована 19 декабря 2008 г.
Образец цитирования:
Michael R. Hoare, Mizan Rahman, “A Probablistic Origin for a New Class of Bivariate Polynomials”, SIGMA, 4 (2008), 089, 18 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma342 https://www.mathnet.ru/rus/sigma/v4/p89
|
|