A Probablistic Origin for a New Class of Bivariate Polynomials
| dc.creator | Hoare, Michael R. | |
| dc.creator | Rahman, Mizan | |
| dc.date | 2008-12-19 | |
| dc.date.accessioned | 2026-07-07T12:20:56Z | |
| dc.date.available | 2026-07-07T12:20:56Z | |
| dc.description | 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. | |
| dc.description | This is a contribution to the Special Issue on Dunkl Operators and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/ | |
| dc.identifier | https://arxiv.org/abs/0812.3879 | |
| dc.identifier | http://arxiv.org/abs/0812.3879 | |
| dc.identifier | SIGMA 4 (2008), 089, 18 pages | |
| dc.identifier | doi:10.3842/SIGMA.2008.089 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/213213 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Probability | |
| dc.title | A Probablistic Origin for a New Class of Bivariate Polynomials | |
| dc.type | text |