Наукова електронна бібліотека
періодичних видань НАН України
періодичних видань НАН України
On a Family of 2-Variable Orthogonal Krawtchouk Polynomials
Репозиторій DSpace/Manakin
- Домашня сторінка
- →
- Фізико-технічні та математичні науки
- →
- Відділення математики
- →
- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
- →
- Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6
- →
- Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6, випуск за цей рік
- →
- Переглянути статтю
JavaScript is disabled for your browser. Some features of this site may not work without it.
On a Family of 2-Variable Orthogonal Krawtchouk Polynomials
Інший ID:
2010 Mathematics Subject Classification: 33C45
DOI:10.3842/SIGMA.2010.090
DOI:10.3842/SIGMA.2010.090
Посилання:
On a Family of 2-Variable Orthogonal Krawtchouk Polynomials / F.A. Grünbaum, M. Rahman // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 19 назв. — англ.
Підтримка:
We thank one referee in particular for a very methodical job that has rendered this into a more accurate paper. In an area where several people have made important contributions he has helped us tell the story properly.
The research of the first author was supported in part by the Applied Math. Sciences
subprogram of the Of fice of Energy Research, USDOE, under Contract DE-AC03-76SF00098, and by AFOSR under contract FA9550-08-1-0169.
Дата:
2010
Переглядів:
519
Завантажень:
189
Анотація:
We give a hypergeometric proof involving a family of 2-variable Krawtchouk polynomials that were obtained earlier by Hoare and Rahman [SIGMA 4 (2008), 089, 18 pages] as a limit of the 9−j symbols of quantum angular momentum theory, and shown to be eigenfunctions of the transition probability kernel corresponding to a ''poker dice'' type probability model. The proof in this paper derives and makes use of the necessary and sufficient conditions of orthogonality in establishing orthogonality as well as indicating their geometrical significance. We also derive a 5-term recurrence relation satisfied by these polynomials.
